U32div.shl_ts: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend as U32div
Lines 136-142 of bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend&start_line=136&end_line=142

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S
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
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD

def shl_ts(+p: Nat, +q: Word(p), +b: U32, +t: Bool, +s: Word(32n), +a0: Bool, +hi: Word(p), +r: Nat, +one: Nat, +h1: {one == 1n : Nat}, +he: {Nat.add(Nat.mul(S.unsigned(p, q), v(b)), r) == S.unsigned(p, hi) : Nat}, +hr: {Nat.is_lt(r, v(b)) == True{} : Bool}, +hts: {Nat.add(WD.uw(32n, s), WD.sc(32n, WD.bo(t, one))) == Nat.add(S.bit_value(a0), Nat.double(r)) : Nat}) -> inv(1n+p, WCon{a0, hi}, v(b), U32.divmod.go.fin(p, q, U32{s}, b, Bool.or(t, U32.is_ge(U32{s}, b)))):
  match t:
    case True{}:
      fin_true(p, q, U32{s}, b, a0, hi, r, one, h1, he, hr, L.subst(Nat, z => {Nat.add(z, WD.sc(32n, one)) == Nat.add(S.bit_value(a0), Nat.double(r)) : Nat}, WD.uw(32n, s), v(U32{s}), Equal.sym(Nat, v(U32{s}), WD.uw(32n, s), vw(s)), hts))
    case False{}:
      +hs = Equal.trans(Nat, v(U32{s}), WD.uw(32n, s), Nat.add(S.bit_value(a0), Nat.double(r)), vw(s), Equal.trans(Nat, WD.uw(32n, s), Nat.add(WD.uw(32n, s), 0n), Nat.add(S.bit_value(a0), Nat.double(r)), Equal.sym(Nat, Nat.add(WD.uw(32n, s), 0n), WD.uw(32n, s), N.add_zero(WD.uw(32n, s))), hts))
      fin_false(p, q, U32{s}, b, a0, hi, r, he, hr, hs, U32.is_ge(U32{s}, b), {==})

Uses (26):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.or
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  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=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.divmod.go.fin
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_ge
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Con
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=bit_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=unsigned
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend&name=fin_false
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend&name=fin_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend&name=inv
  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=vw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend&name=bo
  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/word.bend&name=uw