Skip to content

Fix to the definitions of min and max #1270

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
mortberg merged 1 commit into from
Dec 31, 2025
+9 −6
Merged

Fix to the definitions of min and max #1270

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
12 changes: 6 additions & 6 deletions Cubical/Data/Nat/Properties.agda
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -23,9 +23,9 @@ private
min : ℕ → ℕ → ℕ
min zero m = zero
min (suc n) zero = zero
min (suc n) (suc m) with n <ᵇ m
... | false = suc m
... | true = suc n
min (suc n) (suc m) with n <ᵇ m UsingEq
Comment thread
LorenzoMolena marked this conversation as resolved.
... | false , _ = suc m
... | true , _ = suc n

minSuc : min (suc n) (suc m) ≡ suc (min n m)
minSuc {zero} {zero} = refl
Expand All @@ -44,9 +44,9 @@ minComm (suc n) (suc m) = minSuc ∙∙ cong suc (minComm n m) ∙∙ sym minSuc
max : ℕ → ℕ → ℕ
max zero m = m
max (suc n) zero = suc n
max (suc n) (suc m) with n <ᵇ m
... | false = suc n
... | true = suc m
max (suc n) (suc m) with n <ᵇ m UsingEq
... | false , _ = suc n
... | true , _ = suc m

maxSuc : max (suc n) (suc m) ≡ suc (max n m)
maxSuc {zero} {zero} = refl
Expand Down
3 changes: 3 additions & 0 deletions Cubical/Foundations/Prelude.agda
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -506,6 +506,9 @@ infixl 0 _i0:>_UsingEqP

-- Similar to `inspect`, but more convenient when `a` is not a function
-- application, or when the applied function is not relevant
-- Note: when defining a term with `UsingEq`, it's still possible to prove its properties
-- using a with-abstraction without `UsingEq`, but not the other way around.
-- See `min`/`max` and their properties in Data.Nat.Properties for examples of this.
_UsingEq : (a : A) → singl a
a UsingEq = isContrSingl a .fst

Expand Down