ReduceFiberProof.lt_succ_eq: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend as ReduceFiberProof
Lines 26-40 of bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend&start_line=26&end_line=40

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

def lt_succ_eq(+r: Nat, +size: Nat, below: {Nat.is_lt(r, size) == True{} : Bool},
  not_below: {False{} == Nat.is_lt(1n+r, size) : Bool}) -> {size == 1n+r : Nat}:
  match r size:
    case 0n 0n:
      Empty.absurd({0n == 1n : Nat}, Arith.clash(below))
    case 0n 1n+s:
      match s:
        case 0n:
          {==}
        case 1n+t:
          Empty.absurd({2n+t == 1n : Nat}, Arith.clash(not_below))
    case 1n+p 0n:
      Empty.absurd({0n == 2n+p : Nat}, Arith.clash(below))
    case 1n+p 1n+s:
      Equal.cong(Nat, Nat, n => 1n+n, s, 1n+p, lt_succ_eq(p, s, below, not_below))

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=Equal.cong
  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_lt
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=clash