def off.min_le

bend-osdev-bytes@0.1.1.0 · PROOF.bend:807

import Base

807# n <= k: min(n, k) == n
808def off.min_le(+n: Nat, +k: Nat) -> {Nat.is_le(n, k) == True{} : Bool} -> {Nat.min(n, k) == n : Nat}:
809  match n k:
810    case 0n _:
811      h => {==}
812    case 1n+p 0n:
813      h => off.no({Nat.min(1n+p, 0n) == 1n+p : Nat}, h)
814    case 1n+p 1n+q:
815      h => Equal.cong(Nat, Nat, x => 1n+x, Nat.min(p, q), p, off.min_le(p, q, h))