Commit 24d6caf1 by Guillaume Melquiond

Complete the Coq realizations of theory real.

parent 62c66d4a
 ... ... @@ -61,6 +61,13 @@ Proof. exact opp_IZR. Qed. (* Why3 goal *) Lemma Injective : forall (x:Z) (y:Z), ((BuiltIn.IZR x) = (BuiltIn.IZR y)) -> (x = y). Proof. exact eq_IZR. Qed. (* Why3 goal *) Lemma Monotonic : forall (x:Z) (y:Z), (x <= y)%Z -> ((BuiltIn.IZR x) <= (BuiltIn.IZR y))%R. ... ...
 ... ... @@ -16,7 +16,10 @@ Require Reals.Rtrigo_def. Require Reals.Rpower. Require Reals.R_sqrt. Require BuiltIn. Require int.Int. Require int.Power. Require real.Real. Require real.FromInt. Require real.Square. Require real.ExpLog. ... ... @@ -109,3 +112,17 @@ replace (5 / 10)%R with (/ 2)%R by field. now apply Rpower_sqrt. Qed. (* Why3 goal *) Lemma pow_from_int : forall (x:Z) (y:Z), (0%Z < x)%Z -> (0%Z <= y)%Z -> ((Reals.Rpower.Rpower (BuiltIn.IZR x) (BuiltIn.IZR y)) = (BuiltIn.IZR (int.Power.power x y))). Proof. intros x y h1 h2. rewrite <- Z2Nat.id with (1 := h2). rewrite <- pow_IZR. rewrite <- INR_IZR_INZ. apply Rpower_pow. now apply IZR_lt. Qed.
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