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| author |  Jason Gross <jgross@mit.edu> | 2018-10-29 16:45:10 -0400 |
|---|---|---|
| committer | Jason Gross <jgross@mit.edu> | 2018-10-29 16:45:10 -0400 |
| commit | 063c874f4bd87911cff3466542d599b579f2ff2d (patch) | |
| tree | 11971998bd4a6c124584728ad0ba657eec6c127d | |
| parent | c706f79e31c362c282c7ba991bb364853f06e94b (diff) | |
Add some lemmas about ex, and, eq
| -rw-r--r-- | _CoqProject | 1 | ||||
| -rw-r--r-- | src/Util/Logic/ExistsEqAnd.v | 26 |
2 files changed, 27 insertions, 0 deletions
diff --git a/_CoqProject b/_CoqProject index 54f1cd4f7..659c23407 100644 --- a/_CoqProject +++ b/_CoqProject @@ -6546,6 +6546,7 @@ src/Util/ListUtil/FoldBool.v src/Util/ListUtil/Forall.v src/Util/ListUtil/ForallIn.v src/Util/ListUtil/SetoidList.v +src/Util/Logic/ExistsEqAnd.v src/Util/Logic/ImplAnd.v src/Util/Logic/ProdForall.v src/Util/MSetPositive/Equality.v diff --git a/src/Util/Logic/ExistsEqAnd.v b/src/Util/Logic/ExistsEqAnd.v new file mode 100644 index 000000000..27f08eb89 --- /dev/null +++ b/src/Util/Logic/ExistsEqAnd.v @@ -0,0 +1,26 @@ +Require Import Crypto.Util.FixCoqMistakes. +Require Import Crypto.Util.Tactics.DestructHead. + +Local Ltac t := + repeat first [ progress destruct_head'_ex + | progress destruct_head'_and + | progress intros + | progress subst + | assumption + | progress repeat esplit ]. + +Lemma ex_and_eq_l_iff {A P x} + : (exists y : A, y = x /\ P y) <-> P x. +Proof. t. Qed. + +Lemma ex_and_eq_r_iff {A P x} + : (exists y : A, x = y /\ P y) <-> P x. +Proof. t. Qed. + +Lemma ex_eq_and_l_iff {A P x} + : (exists y : A, P y /\ y = x) <-> P x. +Proof. t. Qed. + +Lemma ex_eq_and_r_iff {A P x} + : (exists y : A, P y /\ x = y) <-> P x. +Proof. t. Qed. |