PROOF.u32.gt_le_ne: def of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/PROOF.bend as PROOF
Lines 996-998 of bend-osdev-algo@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&start_line=996&end_line=998

import Base

def u32.gt_le_ne(+a: U32, +b: U32, +k: U32, e: {U32.is_lt(a, k) == False{} : Bool}, f: {U32.is_eq(a, k) == False{} : Bool}, g: {U32.is_le(a, b) == True{} : Bool}) -> {U32.is_eq(b, k) == False{} : Bool}:
  %Equal.sym(Cmp, U32.cmp(b, k), Nat.cmp(U32.to_nat(b), U32.to_nat(k)), u32.cmp_nat(b, k)) : {Cmp.is_eq(_) == False{} : Bool}
  nat.gt_le_ne(U32.to_nat(a), U32.to_nat(b), U32.to_nat(k), u32.mv_lt(a, k, False{}, e), u32.mv_eq(a, k, False{}, f), u32.mv_le(a, b, True{}, g))

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp.is_eq
  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.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=nat.gt_le_ne
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=u32.cmp_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=u32.mv_eq
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=u32.mv_le
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=u32.mv_lt