PROOFDiv.wd.sel: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/PROOF_div.bend as PROOFDiv
Lines 291-296 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=291&end_line=296

import Base
import bend-osdev-u32@0.1.0.0/u32.bend as U
import bend-osdev-word64@0.1.1.0/word64.bend as W
import bend-osdev-word64@0.1.1.0/LAWS.bend as WB

def wd.sel(g: Bool, +r2: W.W64, +b: W.W64) -> {Nat.add(W.W64.to_nat(W.W64.sel(g, W.W64.sub(r2, b), r2)), Nat.mul(U.U32Nat.bit(g), W.W64.to_nat(b))) == Nat.add(W.W64.to_nat(r2), U.U32Nat.dbl(64n, Nat.mul(U.U32Nat.bit(g), U.U32Nat.bit(W.W64.is_lt(r2, b))))) : Nat}:
  match g:
    case True{}:
      Equal.trans(Nat, Nat.add(W.W64.to_nat(W.W64.sub(r2, b)), Nat.mul(1n, W.W64.to_nat(b))), Nat.add(W.W64.to_nat(r2), U.U32Nat.dbl(64n, U.U32Nat.bit(W.W64.is_lt(r2, b)))), Nat.add(W.W64.to_nat(r2), U.U32Nat.dbl(64n, Nat.mul(1n, U.U32Nat.bit(W.W64.is_lt(r2, b))))), Equal.trans(Nat, Nat.add(W.W64.to_nat(W.W64.sub(r2, b)), Nat.mul(1n, W.W64.to_nat(b))), Nat.add(W.W64.to_nat(W.W64.sub(r2, b)), W.W64.to_nat(b)), Nat.add(W.W64.to_nat(r2), U.U32Nat.dbl(64n, U.U32Nat.bit(W.W64.is_lt(r2, b)))), Equal.cong(Nat, Nat, zz => Nat.add(W.W64.to_nat(W.W64.sub(r2, b)), zz), Nat.mul(1n, W.W64.to_nat(b)), W.W64.to_nat(b), wr.d5(W.W64.to_nat(b))), WB.sub_wrap(r2, b)), Equal.cong(Nat, Nat, zz => Nat.add(W.W64.to_nat(r2), U.U32Nat.dbl(64n, zz)), U.U32Nat.bit(W.W64.is_lt(r2, b)), Nat.mul(1n, U.U32Nat.bit(W.W64.is_lt(r2, b))), wr.d6(U.U32Nat.bit(W.W64.is_lt(r2, b)))))
    case False{}:
      wr.d7(W.W64.to_nat(r2), W.W64.to_nat(b), U.U32Nat.bit(W.W64.is_lt(r2, b)))

Uses (17):
  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.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.mul
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.bit
  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/LAWS.bend&name=sub_wrap
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/PROOF_div.bend&name=wr.d5
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/PROOF_div.bend&name=wr.d6
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/PROOF_div.bend&name=wr.d7
  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.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.sel
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.sub
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.to_nat