SignedPROOF.not_le_add: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend as SignedPROOF
Lines 273-285 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=273&end_line=285

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

def not_le_add(+a: Nat, +b: Nat, +c: Nat, h: {Nat.is_le(a, c) == False{} : Bool}) ->
  {Nat.is_le(Nat.add(a, b), c) == False{} : Bool}:
  match a:
    case 0n:
      Empty.absurd({Nat.is_le(Nat.add(0n, b), c) == False{} : Bool},
        Arith.clash_true(Equal.trans(Bool, True{}, Nat.is_le(0n, c), False{},
          Equal.sym(Bool, Nat.is_le(0n, c), True{}, Arith.le_zero(c)), h)))
    case 1n+p:
      match c:
        case 0n:
          {==}
        case 1n+q:
          not_le_add(p, b, q, h)

Uses (9):
  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=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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=clash_true
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=le_zero