SignedPROOF.lt_not_le: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend as SignedPROOF
Lines 287-301 of bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend&start_line=287&end_line=301

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

# b < a gives a <= b false.
def lt_not_le(+b: Nat, +a: Nat, h: {Nat.is_lt(b, a) == True{} : Bool}) -> {Nat.is_le(a, b) == False{} : Bool}:
  match b:
    case 0n:
      match a:
        case 0n:
          Empty.absurd({Nat.is_le(0n, 0n) == False{} : Bool}, Arith.clash(h))
        case 1n+q:
          {==}
    case 1n+p:
      match a:
        case 0n:
          Empty.absurd({Nat.is_le(0n, 1n+p) == False{} : Bool}, Arith.clash(h))
        case 1n+q:
          lt_not_le(p, q, h)

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_le
  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/storage/arith.bend&name=clash