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Unary integers #1964

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Merged
Alizter merged 8 commits into from
May 23, 2024
Merged

Unary integers #1964

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0938eee
Unary integers
Alizter May 16, 2024
d86c4fb
review suggestions
Alizter May 19, 2024
deaf702
define Int add/mul by induction
Alizter May 20, 2024
0811b18
3 constructor definition of Int
Alizter May 22, 2024
8a66911
more comments
Alizter May 22, 2024
85090ef
fix whitespace
Alizter May 22, 2024
d02a547
Spaces/Int: minor clean-ups
jdchristensen May 23, 2024
4a389b4
open and delimit scope after declaration
Alizter May 23, 2024
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10 changes: 7 additions & 3 deletions theories/Basics/Decidable.v
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Original file line number Diff line number Diff line change
Expand Up @@ -121,14 +121,18 @@ Global Instance decidable_empty : Decidable Empty

(** ** Transfer along equivalences *)

Definition decidable_equiv (A : Type) {B : Type} (f : A -> B) `{IsEquiv A B f}
: Decidable A -> Decidable B.
Definition decidable_iff {A B} (f : A -> B) (f' : B -> A)
: Decidable A -> Decidable B.
Proof.
intros [a|na].
- exact (inl (f a)).
- exact (inr (fun b => na (f^-1 b))).
- exact (inr (fun b => na (f' b))).
Defined.

Definition decidable_equiv (A : Type) {B : Type} (f : A -> B) `{IsEquiv A B f}
: Decidable A -> Decidable B
:= decidable_iff f f^-1.

Definition decidable_equiv' (A : Type) {B : Type} (f : A <~> B)
: Decidable A -> Decidable B
:= decidable_equiv A f.
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