SlicePROOF.min_pick: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend as SlicePROOF
Lines 280-291 of bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend&start_line=280&end_line=291

import Base

def min_pick(+a: Nat, +b: Nat) -> {Nat.min(a, b) == Bool.pick(Nat, Nat.is_le(a, b), a, b) : Nat}:
  match a b:
    case 0n 0n:
      {==}
    case 0n 1n+q:
      {==}
    case 1n+p 0n:
      {==}
    case 1n+p 1n+q:
      Equal.trans(Nat, 1n+Nat.min(p, q), 1n+Bool.pick(Nat, Nat.is_le(p, q), p, q), Bool.pick(Nat, Nat.is_le(p, q), 1n+p, 1n+q),
        Equal.cong(Nat, Nat, x => 1n+x, Nat.min(p, q), Bool.pick(Nat, Nat.is_le(p, q), p, q), min_pick(p, q)),
        Equal.sym(Nat, Bool.pick(Nat, Nat.is_le(p, q), 1n+p, 1n+q), 1n+Bool.pick(Nat, Nat.is_le(p, q), p, q), pick_succ(Nat.is_le(p, q), p, q)))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.pick
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.min
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend&name=pick_succ