fact stringlengths 12 6.75k | type stringclasses 14
values | library stringclasses 3
values | imports listlengths 0 17 | filename stringclasses 26
values | symbolic_name stringlengths 2 34 | docstring stringclasses 1
value |
|---|---|---|---|---|---|---|
case_split_concl_on ind := case_split_concl_on_gen sdestruct ind. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | case_split_concl_on | |
case_split_concl_on_dep ind := case_split_concl_on_gen sdepdestruct ind. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | case_split_concl_on_dep | |
case_splitting_concl_on t := repeat (case_split_concl_on t; ssubst; simpl). | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | case_splitting_concl_on | |
case_splitting_concl_on_nored t := repeat (case_split_concl_on t; ssubst). | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | case_splitting_concl_on_nored | |
case_splitting_concl_on_dep t := repeat (case_split_concl_on_dep t; ssubst; simpl). | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | case_splitting_concl_on_dep | |
case_splitting_concl_on_dep_nored t := repeat (case_split_concl_on_dep t; ssubst). | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | case_splitting_concl_on_dep_nored | |
generalizing := repeat match goal with | [ H : _ |- _ ] => generalize H; clear H end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | generalizing | |
fsolve := solve [ eassumption | symmetry; eassumption | econstructor ]. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | fsolve | |
full_inst e tac := let tpe := type of e in lazymatch tpe with | ?T -> ?Q => cut T; [ let H := fresh "H" in intro H; full_inst (e H) tac; clear H | try fsolve ] | forall x : ?T, _ => let v := fresh "v" in evar (v : T); let v2 := (eval unfold v in v) in clear v; full_inst (e v2) tac; try match goal with | [ y : T |- _ ] ... | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | full_inst | |
sinv_gen dep H := lazymatch dep with | true => depelim H | false => inversion H end; ssubst. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | sinv_gen | |
sdestr_gen dep H := let ty := type of H in tryif isIndexedInd ty then lazymatch dep with | true => depelim H | false => dependent inversion H end; ssubst else destruct H. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | sdestr_gen | |
sinvert_gen dep H := let intro_invert tt := let H1 := fresh "H" in intro H1; sinv_gen dep H1; try clear H1 in lazymatch type of H with | _ -> _ => full_inst H intro_invert | _ => lazymatch goal with | [ |- context[H] ] => sdestr_gen dep H | [ |- _ ] => let ty := type of H in sinv_gen dep H; tryif clear H then notHyp ty... | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | sinvert_gen | |
sinvert H := sinvert_gen false H. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | sinvert | |
sdepinvert H := sinvert_gen true H. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | sdepinvert | |
full_einst e tac := let tpe := type of e in lazymatch tpe with | ?T -> ?Q => cut T; [ let H := fresh "H" in intro H; full_einst (e H) tac; clear H | try fsolve ] | forall x : ?T, _ => let v := fresh "v" in evar (v : T); let v2 := (eval unfold v in v) in clear v; full_einst (e v2) tac | _ => generalize e; tac tt; try fs... | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | full_einst | |
seinvert_gen dep H := let intro_invert tt := let H1 := fresh "H" in intro H1; sinv_gen dep H1; try clear H1 in lazymatch type of H with | _ -> _ => full_einst H intro_invert | _ => lazymatch goal with | [ |- context[H] ] => sdestr_gen dep H | [ |- _ ] => let ty := type of H in sinv_gen dep H; tryif clear H then noteHyp... | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | seinvert_gen | |
seinvert H := seinvert_gen false H. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | seinvert | |
sedepinvert H := seinvert_gen true H. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | sedepinvert | |
rdone {T : Type} (x : T) := True. | Definition | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | rdone | |
un_done := repeat match goal with | [ H : rdone _ |- _ ] => clear H end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | un_done | |
impl_fwd e := match type of e with | ?T -> ?Q => impl_fwd (e ltac:(fsolve)) | _ => generalize e end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | impl_fwd | |
forward_base tac e := lazymatch type of e with | ?P -> ?Q => fail | _ => let rec fwd e := lazymatch type of e with | ?P -> ?Q => impl_fwd (e (ltac:(fsolve))) | forall x : ?T, _ => let v := fresh "v" in evar (v : T); let v2 := (eval unfold v in v) in clear v; fwd (e v2); try match goal with | [ y : T |- _ ] => unify y v... | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | forward_base | |
forward H := forward_base ltac:(simpl) H. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | forward | |
forward_nored H := forward_base ltac:(idtac) H. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | forward_nored | |
forwarding := repeat match goal with | [ H : forall x : _,_ |- _ ] => forward H end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | forwarding | |
forwarding_nored := repeat match goal with | [ H : forall x : _,_ |- _ ] => forward_nored H end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | forwarding_nored | |
inList x lst := lazymatch lst with | (?t, ?y) => tryif constr_eq x y then idtac else inList x t | x => idtac | _ => fail end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | inList | |
notInList x lst := tryif inList x lst then fail else idtac. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | notInList | |
all f ls := match ls with | (?LS, ?X) => f X; all f LS | (_, _) => fail 1 | _ => f ls end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | all | |
lst_rev lst := let rec hlp lst acc := match lst with | tt => acc | (?t, ?h) => hlp t (acc, h) | ?x => constr:((acc, x)) end in hlp lst tt. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | lst_rev | |
with_hyps p f := let rec hlp acc := match goal with | [ H : ?P |- _ ] => p P; notInList H acc; hlp (acc, H) | _ => f ltac:(lst_rev acc) end in hlp tt. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | with_hyps | |
with_prop_hyps := with_hyps isProp. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | with_prop_hyps | |
all_hyps f := with_hyps ltac:(fun _ => idtac) ltac:(all f). | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | all_hyps | |
all_prop_hyps f := with_prop_hyps ltac:(all f). | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | all_prop_hyps | |
qforward H := lazymatch type of H with | ?P -> ?Q => fail | _ => einst H; progress repeat match goal with | [ H0 : ?P |- (?Q -> _) -> _ ] => unify P Q; let H1 := fresh "H" in intro H1; generalize (H1 H0); clear H1 end; match goal with | [ |- ?P -> _ ] => notTrivial P; noEvars P; notHyp P end; intro end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | qforward | |
qforwarding := all_hyps ltac:(fun H => try qforward H). Tactic Notation "forward_reasoning" int_or_var(n) := do n qforwarding. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | qforwarding | |
inster0 e trace := match type of e with | forall x : ?T, _ => match goal with | [ H : _ |- _ ] => inster0 (e H) (trace, H) | _ => isProp T; let H := fresh "H" in assert (H: T) by isolve; inster0 (e H) (trace, H) | _ => fail 2 end | _ => match trace with | (_, _) => match goal with | [ H : rdone (trace, _) |- _ ] => fai... | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | inster0 | |
inster H := inster0 H H. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | inster | |
instering := repeat match goal with | [ H : ?T |- _ ] => isProp T; inster H end; un_done. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | instering | |
einster e := let tpe := type of e in lazymatch tpe with | ?T -> ?Q => let H := fresh "H" in tryif (assert (H : T) by isolve) then einster (e H); clear H else noteHyp tpe; generalize e; intro | forall x : ?T, _ => let v := fresh "v" in evar (v : T); let v2 := (eval unfold v in v) in clear v; einster (e v2) | _ => noteHy... | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | einster | |
einstering := repeat match goal with | [ H : ?P |- _ ] => isProp P; einster H end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | einstering | |
srewrite H := (erewrite H in * by isolve_nolia) || (erewrite <- H in * by isolve_nolia). | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | srewrite | |
srewrite_in_concl H := (erewrite H by isolve_nolia) || (erewrite <- H by isolve_nolia). | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | srewrite_in_concl | |
srewriting := repeat match goal with | [ H : ?T |- _ ] => checkTargetLPO T; erewrite H in * by isolve_nolia | [ H : ?T |- _ ] => checkTargetRevLPO T; erewrite <- H in * by isolve_nolia end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | srewriting | |
red_in_all := simpl in *. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | red_in_all | |
red_in_concl := simpl. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | red_in_concl | |
destruct_sigma_in_goal := repeat match goal with | [ |- context[proj1_sig ?X] ] => destruct X; simpl end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | destruct_sigma_in_goal | |
destruct_sigma := repeat match goal with | [H : context[proj1_sig ?X] |- _] => destruct X; simpl in * | [ |- context[proj1_sig ?X] ] => destruct X; simpl in * end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | destruct_sigma | |
destruct_sigma_dep_in_goal := repeat match goal with | [ |- context[proj1_sig ?X] ] => dep_destruct X; simpl end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | destruct_sigma_dep_in_goal | |
destruct_sigma_dep := repeat match goal with | [H : context[proj1_sig ?X] |- _] => dep_destruct X; simpl in * | [ |- context[proj1_sig ?X] ] => dep_destruct X; simpl in * end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | destruct_sigma_dep | |
invert_sigma := repeat match goal with | [ H: exist _ _ _ = exist _ _ _ |- _ ] => induction H using eq_sig_rect; ssubst; simpl in * | [ H: existT _ _ _ = existT _ _ _ |- _ ] => induction H using eq_sigT_rect; ssubst; simpl in * end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | invert_sigma | |
simpl_sigma := invert_sigma; destruct_sigma. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | simpl_sigma | |
unfold_local_defs := repeat match goal with | [f := _ |- _] => unfold f in *; try clear f end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | unfold_local_defs | |
generalize_proofs_in t := lazymatch t with | ?X ?Y => (tryif is_var Y then idtac else let ty := type of Y in lazymatch type of ty with | Prop => try generalize Y | _ => generalize_proofs_in Y end); generalize_proofs_in X | ?X -> ?Y => generalize_proofs_in X; generalize_proofs_in Y | _ => idtac end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | generalize_proofs_in | |
generalize_proofs_in_goal := match goal with | [|- ?G] => generalize_proofs_in G end. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | generalize_proofs_in_goal | |
generalize_proofs_in_hyp H := let T := type of H in try (revert H; progress generalize_proofs_in T). | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | generalize_proofs_in_hyp | |
generalize_proofs := generalize_proofs_in_goal; repeat match goal with | [H: ?T |- _] => revert H; progress generalize_proofs_in T end. Tactic Notation "generalize" "proofs" := generalize_proofs_in_goal. Tactic Notation "generalize" "proofs" "in" ident(H) := generalize_proofs_in_hyp H. Tactic Notation "generalize" "pro... | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | generalize_proofs | |
use_tac := let H := fresh "H" in intro H; try move H at top; try simp_hyp H. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | use_tac | |
congr_tac := congruence 400. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | congr_tac | |
lia_tac := lia. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | lia_tac | |
f_equal_tac := f_equal. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | f_equal_tac | |
firstorder_tac := solve [ firstorder (trysolve; auto) ]. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | firstorder_tac | |
firstorder_nolia_tac := solve [ firstorder (trysolve_nolia; auto) ]. Declare ML Module "coq-hammer-tactics.plugin". | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | firstorder_nolia_tac | |
sauto_tac := sauto. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | sauto_tac | |
sdone_tac := solve [ trysolve ]. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | sdone_tac | |
sdone_nolia_tac := solve [ trysolve_nolia ]. Tactic Notation "sdone" := sdone_tac. Tactic Notation "sdone" "lia:" "on" := sdone_tac. Tactic Notation "sdone" "lia:" "off" := sdone_nolia_tac. | Ltac | theories | [
"Require Import Lia.",
"From Stdlib.Program Require Import Equality.",
"From Hammer Require Import Tactics."
] | theories/Tactics/Tactics.v | sdone_nolia_tac |
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