PROOFDiv.wd.top: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/PROOF_div.bend as PROOFDiv
Lines 127-129 of bend-osdev-word64@0.1.1.0/PROOF_div.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/PROOF_div.bend&start_line=127&end_line=129

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@0.1.1.0/word64.bend as W

# the top bit of a word, below 2
def wd.top(+x: W.W64) -> {Nat.is_lt(U32.to_nat(U32.shrn(W.W64.hi(x), 31n)), U.U32Nat.dbl(1n, 1n)) == True{} : Bool}:
  Equal.trans(Bool, Nat.is_lt(U32.to_nat(U32.shrn(W.W64.hi(x), 31n)), U.U32Nat.dbl(1n, 1n)), Nat.is_lt(U.U32Nat.high(31n, U32.to_nat(W.W64.hi(x))), U.U32Nat.dbl(1n, 1n)), True{}, Equal.cong(Nat, Bool, zz => Nat.is_lt(zz, U.U32Nat.dbl(1n, 1n)), U32.to_nat(U32.shrn(W.W64.hi(x), 31n)), U.U32Nat.high(31n, U32.to_nat(W.W64.hi(x))), Equal.sym(Nat, U.U32Nat.high(31n, U32.to_nat(W.W64.hi(x))), U32.to_nat(U32.shrn(W.W64.hi(x), 31n)), Equal.sym(Nat, U32.to_nat(U32.shrn(W.W64.hi(x), 31n)), U.U32Nat.high(31n, U32.to_nat(W.W64.hi(x))), UL.u32_shrn_value(W.W64.hi(x), 31n)))), UL.high_lt(31n, 1n, 32n, U32.to_nat(W.W64.hi(x)), {==}, wu.lt(W.W64.hi(x))))

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.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shrn
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=high_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=u32_shrn_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-u32@0.1.0.0/u32.bend&name=U32Nat.high
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/PROOF_div.bend&name=wu.lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.hi