SlicePROOF.min_mono: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend as SlicePROOF
Lines 54-64 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=54&end_line=64

import Base
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith

# min(a, b) <= min(c, b) for a <= c.
def min_mono(+a: Nat, +c: Nat, +b: Nat, h: {Nat.is_le(a, c) == True{} : Bool}) -> {Nat.is_le(Nat.min(a, b), Nat.min(c, b)) == True{} : Bool}:
  match a c b:
    case 0n _ _:
      Arith.le_zero(Nat.min(c, b))
    case 1n+p 0n _:
      Empty.absurd({Nat.is_le(Nat.min(1n+p, b), Nat.min(0n, b)) == True{} : Bool}, Arith.clash(h))
    case 1n+p 1n+q 0n:
      {==}
    case 1n+p 1n+q 1n+r:
      min_mono(p, q, r, h)

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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/storage/arith.bend&name=clash
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=le_zero