Commit 2a3675a5 authored by Guillaume Melquiond's avatar Guillaume Melquiond

Added Zpower_ge_0.

parent 12e022e0
......@@ -2159,6 +2159,19 @@ easy.
now apply Zpower_gt_1.
Qed.
Theorem Zpower_ge_0 :
forall e,
(0 <= Zpower r e)%Z.
Proof.
intros [|e|e].
apply Zle_0_1.
apply le_Z2R.
rewrite Z2R_Zpower.
apply bpow_ge_0.
discriminate.
apply Zle_refl.
Qed.
Theorem Zpower_Zpower_nat :
forall b e, (0 <= e)%Z ->
Zpower b e = Zpower_nat b (Zabs_nat e).
......
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