def earlier_different

bendtorch-core@0.1.0.0 · src/tensor/matmul_PROOF.bend:290

import Base

290def earlier_different(+a: Nat, +b: Nat, earlier: {Nat.is_lt(a, b) == True{} : Bool}) -> {Nat.is_eq(b, a) == False{} : Bool}:
291  match a b:
292    case 0n 0n:
293      Empty.absurd({Nat.is_eq(0n, 0n) == False{} : Bool}, no_earlier_zero(0n, earlier))
294    case 0n 1n+q:
295      {==}
296    case 1n+p 0n:
297      Empty.absurd({Nat.is_eq(0n, 1n+p) == False{} : Bool}, no_earlier_zero(1n+p, earlier))
298    case 1n+p 1n+q:
299      earlier_different(p, q, earlier)