U64.add_lt1: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend as U64
Lines 179-181 of bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend&start_line=179&end_line=181

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend as U3
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend as UD

def add_lt1(+one: Nat, +h1: {one == 1n : Nat}, +x: U32, +y: U32) -> {U32.is_lt(U32.add(x, y), x) == carry32(x, y) : Bool}:
  %Equal.sym(Bool, U32.is_lt(U32.add(x, y), x), Nat.is_lt(UD.v(U32.add(x, y)), UD.v(x)), U3.is_lt_nat(U32.add(x, y), x)) : {_ == carry32(x, y) : Bool}
  WD.carry_lt(32n, one, h1, UD.v(U32.add(x, y)), UD.v(x), UD.v(y), carry32(x, y), add_cons(x, y), UD.vb(one, h1, y))

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=is_lt_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend&name=vb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend&name=carry_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend&name=add_cons
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend&name=carry32