MatmulPROOF.earlier_different: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend as MatmulPROOF
Lines 290-299 of bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&start_line=290&end_line=299

import Base

def earlier_different(+a: Nat, +b: Nat, earlier: {Nat.is_lt(a, b) == True{} : Bool}) -> {Nat.is_eq(b, a) == False{} : Bool}:
  match a b:
    case 0n 0n:
      Empty.absurd({Nat.is_eq(0n, 0n) == False{} : Bool}, no_earlier_zero(0n, earlier))
    case 0n 1n+q:
      {==}
    case 1n+p 0n:
      Empty.absurd({Nat.is_eq(0n, 1n+p) == False{} : Bool}, no_earlier_zero(1n+p, earlier))
    case 1n+p 1n+q:
      earlier_different(p, q, earlier)

Uses (6):
  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_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=no_earlier_zero