diff options
Diffstat (limited to 'src/QInst.v')
| -rw-r--r-- | src/QInst.v | 43 |
1 files changed, 42 insertions, 1 deletions
diff --git a/src/QInst.v b/src/QInst.v index 1c0016c..14ff0f7 100644 --- a/src/QInst.v +++ b/src/QInst.v @@ -29,7 +29,7 @@ Qed. Hint Resolve impl_split : smtcoq_core. -(* verit silently transforms an <implb (a || b) c> into a <or (not a) c> +(** verit silently transforms an <implb (a || b) c> into a <or (not a) c> or into a <or (not b) c> when instantiating such a quantified theorem *) Lemma impl_or_split_right a b c: implb (a || b) c = true -> negb b || c = true. @@ -45,6 +45,35 @@ Proof. destruct a; destruct c; intuition. Qed. +(** same for Boolean equivalence, modulo symmetry *) +Lemma eqb_sym_or_split_right a b c: + Bool.eqb c (a || b) = true -> negb b || c = true. +Proof. + intro H. + destruct a; destruct c; intuition. +Qed. + +Lemma eqb_sym_or_split_left a b c: + Bool.eqb c (a || b) = true -> negb a || c = true. +Proof. + intro H. + destruct a; destruct c; intuition. +Qed. + +Lemma eqb_or_split_right a b c: + Bool.eqb (a || b) c = true -> negb b || c = true. +Proof. + intro H. + destruct a; destruct c; intuition. +Qed. + +Lemma eqb_or_split_left a b c: + Bool.eqb (a || b) c = true -> negb a || c = true. +Proof. + intro H. + destruct a; destruct c; intuition. +Qed. + (** verit considers equality modulo its symmetry, so we have to recover the right direction in the instances of the theorems *) (* TODO: currently incomplete *) @@ -159,6 +188,18 @@ Ltac vauto := | eapply impl_or_split_left; first [ strategy1 H | strategy2 H ] + | eapply eqb_sym_or_split_right; + first [ strategy1 H + | strategy2 H ] + | eapply eqb_sym_or_split_left; + first [ strategy1 H + | strategy2 H ] + | eapply eqb_or_split_right; + first [ strategy1 H + | strategy2 H ] + | eapply eqb_or_split_left; + first [ strategy1 H + | strategy2 H ] ] end ] |