Fixprime.le_c: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend as Fixprime
Lines 121-127 of bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend&start_line=121&end_line=127

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

# is_lt(a, b) is is_le(a + 1, b)
def le_c(+a: Nat, +b: Nat, +d: Bool, +hd: {Nat.is_le(1n+a, b) == d : Bool}, +hc: {Nat.is_lt(a, b) == False{} : Bool}) -> {False{} == d : Bool}:
  match d:
    case False{}:
      {==}
    case True{}:
      Empty.absurd({False{} == True{} : Bool}, L.true_false(Equal.trans(Bool, True{}, Nat.is_lt(a, b), False{}, Equal.sym(Bool, Nat.is_lt(a, b), True{}, N.succ_le_lt(a, b, hd)), hc)))

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.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/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=succ_le_lt