ProofShift.ws.g1b: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_shift.bend as ProofShift
Lines 384-385 of bend-osdev-word64@0.1.1.0/proof_shift.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&start_line=384&end_line=385

import Base
import bend-osdev-u32@0.1.0.0/u32.bend as U

def ws.g1b(+n: Nat, +k: Nat, +w: Word(n), +hk: {Nat.is_le(k, n) == True{} : Bool}) -> {Nat.add(Word.to_nat(n, ws.shl(n, k, w)), U.U32Nat.dbl(n, Word.to_nat(n, ws.shr(n, Nat.sub(n, k), w)))) == U.U32Nat.dbl(k, Word.to_nat(n, w)) : Nat}:
  Equal.trans(Nat, Nat.add(Word.to_nat(n, ws.shl(n, k, w)), U.U32Nat.dbl(n, Word.to_nat(n, ws.shr(n, Nat.sub(n, k), w)))), Nat.add(U.U32Nat.dbl(k, Nat.sub(Word.to_nat(n, w), U.U32Nat.dbl(Nat.sub(n, k), Word.to_nat(n, ws.shr(n, Nat.sub(n, k), w))))), U.U32Nat.dbl(n, Word.to_nat(n, ws.shr(n, Nat.sub(n, k), w)))), U.U32Nat.dbl(k, Word.to_nat(n, w)), Equal.cong(Nat, Nat, v => Nat.add(v, U.U32Nat.dbl(n, Word.to_nat(n, ws.shr(n, Nat.sub(n, k), w)))), Word.to_nat(n, ws.shl(n, k, w)), U.U32Nat.dbl(k, Nat.sub(Word.to_nat(n, w), U.U32Nat.dbl(Nat.sub(n, k), Word.to_nat(n, ws.shr(n, Nat.sub(n, k), w))))), ws.g1a(n, k, w, hk)), Equal.sym(Nat, U.U32Nat.dbl(k, Word.to_nat(n, w)), Nat.add(U.U32Nat.dbl(k, Nat.sub(Word.to_nat(n, w), U.U32Nat.dbl(Nat.sub(n, k), Word.to_nat(n, ws.shr(n, Nat.sub(n, k), w))))), U.U32Nat.dbl(n, Word.to_nat(n, ws.shr(n, Nat.sub(n, k), w)))), ws.g1w(n, k, w, hk)))

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.dbl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&name=ws.g1a
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&name=ws.g1w
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&name=ws.shl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&name=ws.shr