ProofShift.ws.gshr_hi_v: def of bend-osdev-word64@0.1.1.1
Import: import bend-osdev-word64@0.1.1.1/proof_shift.bend as ProofShift
Lines 447-449 of bend-osdev-word64@0.1.1.1/proof_shift.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.1/proof_shift.bend&start_line=447&end_line=449

import Base
import bend-osdev-u32@0.1.0.0/u32.bend as U
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL
import bend-osdev-word64@0.1.1.1/proof_value.bend as P

# a shift right by n <= k: the low half is the high half shifted by k - n
def ws.gshr_hi_v(+n: Nat, +k: Nat, +hw: Word(n)) -> {P.wv.V(n, Word.zero(n), ws.shr(n, Nat.sub(k, n), hw)) == Word.to_nat(n, ws.shr(n, Nat.sub(k, n), hw)) : Nat}:
  Equal.trans(Nat, P.wv.V(n, Word.zero(n), ws.shr(n, Nat.sub(k, n), hw)), Nat.add(Word.to_nat(n, ws.shr(n, Nat.sub(k, n), hw)), U.U32Nat.dbl(n, 0n)), Word.to_nat(n, ws.shr(n, Nat.sub(k, n), hw)), Equal.cong(Nat, Nat, v => Nat.add(Word.to_nat(n, ws.shr(n, Nat.sub(k, n), hw)), U.U32Nat.dbl(n, v)), Word.to_nat(n, Word.zero(n)), 0n, UL.word_zero_value(n)), ns.d0(n, Word.to_nat(n, ws.shr(n, Nat.sub(k, n), hw))))

Uses (13):
  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.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.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=Base/base.bend&name=Word.zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=word_zero_value
  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@0.1.1.1/proof_shift.bend&name=ns.d0
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.1/proof_shift.bend&name=ws.shr
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.1/proof_value.bend&name=wv.V