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Adapt to https://github.com/math-comp/math-comp/pull/1110 #16

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Nov 7, 2023
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2 changes: 1 addition & 1 deletion theories/numbers/ssete7.v
Original file line number Diff line number Diff line change
Expand Up @@ -1309,7 +1309,7 @@ rewrite !muln1 mulnDl mulnC addnCA; congr (_ + _).
Qed.


Lemma F22 n: \sum_(i<n) i `! * i = n `! .-1.
Lemma F22 n: \sum_(i<n) i `! * i = (n `! ).-1.
Proof.
elim: n; first by rewrite big_ord0.
move => n Hrec;rewrite big_ord_recr /= Hrec {Hrec}.
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2 changes: 1 addition & 1 deletion theories/ordinals/sset15.v
Original file line number Diff line number Diff line change
Expand Up @@ -4731,7 +4731,7 @@ move: sc => [ix sx].
have pf':~ (exists a : Set, cpow_less_ec_prop \2c x a).
by move => [a [px py]]; case: pf; exists a.
move: (cpow_less_ec_pr6 ix le22 pf') => eq1.
have pa: (\2c ^c \cf (\2c ^<c x)) <c \2c ^<c x.
have pa: (\2c ^c (\cf (\2c ^<c x))) <c \2c ^<c x.
have pb:= (cofinality_small ix).
move: (aux _ (conj pb sx)) => [b [p1 p2 p3]].
by rewrite eq1; apply: (clt_leT p3); apply: cpow_less_pr2.
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4 changes: 2 additions & 2 deletions theories/sets/sset1.v
Original file line number Diff line number Diff line change
Expand Up @@ -111,7 +111,7 @@ Axiom IM_P : forall (x : Set) (f : x -> Set) (y : Set),

Axiom p_or_not_p: forall P:Prop, P \/ ~ P.

Lemma ixm (P: Prop): P + ~P.
Lemma ixm (P: Prop): P + (~P).
Proof.
apply: (chooseT (fun _ => True)).
by case: (p_or_not_p P) => H;constructor; [ left | right ].
Expand Down Expand Up @@ -1030,7 +1030,7 @@ Definition powerset (x : Set) :=
IM (fun p : x -> C2 =>
Zo x (fun y : Set => forall hyp : inc y x, Ro (p (Bo hyp)) = C0)).

Notation "\Po E" := (powerset E) (at level 40).
Notation "\Po E" := (powerset E) (at level 30).

Lemma setP_i y x : sub y x -> inc y (\Po x).
Proof.
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