Arith.sc_lt_cancel_g: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend as Arith
Lines 47-52 of bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend&start_line=47&end_line=52

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

def sc_lt_cancel_g(+k: Nat, +a: Nat, +b: Nat, +c: Bool, +hc: {Nat.is_lt(a, b) == c : Bool}, +h: {Nat.is_lt(sc(k, a), sc(k, b)) == True{} : Bool}) -> {Nat.is_lt(a, b) == True{} : Bool}:
  match c:
    case True{}:
      hc
    case False{}:
      Empty.absurd({Nat.is_lt(a, b) == True{} : Bool}, L.true_false(Equal.trans(Bool, True{}, Nat.is_le(sc(k, b), sc(k, a)), False{}, Equal.sym(Bool, Nat.is_le(sc(k, b), sc(k, a)), True{}, sc_le(k, b, a, N.not_lt_le(a, b, hc))), N.lt_not_le(sc(k, a), sc(k, b), h))))

Uses (12):
  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.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend&name=sc_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=true_false
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_not_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=not_lt_le