Nat.sub_succ_left: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as Nat
Lines 297-305 of bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&start_line=297&end_line=305

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L

def sub_succ_left(+a: Nat, +b: Nat, e: {Nat.is_le(b, a) == True{} : Bool}) -> {Nat.sub(1n+a, b) == 1n+Nat.sub(a, b) : Nat}:
  match a b:
    case _ 0n:
      %Equal.sym(Nat, Nat.sub(a, 0n), a, sub_zero(a)) : {1n+a == 1n+_ : Nat}
      {==}
    case 0n 1n+q:
      Empty.absurd({Nat.sub(1n, 1n+q) == 1n+Nat.sub(0n, 1n+q) : Nat}, L.false_true(e))
    case 1n+p 1n+q:
      sub_succ_left(p, q, e)

Uses (8):
  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=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.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=sub_zero