Words32.bound32: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/words32.bend as Words32
Lines 98-99 of bend-collections-laws-math@1.0.0.0/proofs/lib/words32.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/words32.bend&start_line=98&end_line=99

import Base
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/nat.bend as N
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC

def bound32(+one: Nat, +h1: {one == 1n : Nat}, +x: Nat, +d: Nat, +hd: {Nat.is_lt(1n+d, 32n) == True{} : Bool}, +hx: {Nat.is_lt(x, SC.pow2(d)) == True{} : Bool}) -> {Nat.is_lt(1n+x, WD.sc(32n, one)) == True{} : Bool}:
  N.le_lt_trans(1n+x, SC.pow2(d), WD.sc(32n, one), N.lt_succ_le_succ(x, SC.pow2(d), hx), N.lt_le_trans(SC.pow2(d), SC.pow2(1n+d), WD.sc(32n, one), N.pow2_lt_succ(d), pow_le32(one, h1, 1n+d, hd)))

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=le_lt_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_succ_le_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=pow2_lt_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/words32.bend&name=pow_le32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=pow2