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classical/unstable.v

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@@ -229,8 +229,7 @@ Inductive boxed T := Box of T.
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Reserved Notation "`1- r" (format "`1- r", at level 2).
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Reserved Notation "f \^-1" (at level 35, format "f \^-1").
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(* TODO: To be backported to finmap *)
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(* PR in progress: https://github.com/math-comp/finmap/pull/149 *)
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Lemma fset_nat_maximum (X : choiceType) (A : {fset X})
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(f : X -> nat) : A != fset0 ->
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(exists i, i \in A /\ forall j, j \in A -> f j <= f i)%nat.
@@ -388,16 +387,19 @@ Qed.
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End order_min.
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(* PR in progress: https://github.com/math-comp/math-comp/pull/1515 *)
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Lemma intrD1 {R : pzRingType} (i : int) : i%:~R + 1 = (i + 1)%:~R :> R.
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Proof. by rewrite intrD. Qed.
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(* PR in progress: https://github.com/math-comp/math-comp/pull/1515 *)
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Lemma intr1D {R : pzRingType} (i : int) : 1 + i%:~R = (1 + i)%:~R :> R.
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Proof. by rewrite intrD. Qed.
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Section trunc_floor_ceil.
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Context {R : archiRealDomainType}.
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Implicit Type x : R.
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(* PR in progress: https://github.com/math-comp/math-comp/pull/1515 *)
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Lemma abs_ceil_ge x : `|x| <= `|Num.ceil x|.+1%:R.
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Proof.
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rewrite -natr1 natr_absz; have [x0|x0] := ltP 0 x.

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