ProofShift.ns.dbl_double: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_shift.bend as ProofShift
Lines 191-196 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=191&end_line=196

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

def ns.dbl_double(m: Nat, +x: Nat) -> {U.U32Nat.dbl(m, Nat.double(x)) == Nat.double(U.U32Nat.dbl(m, x)) : Nat}:
  match m:
    case 0n:
      {==}
    case 1n+ +p:
      Equal.cong(Nat, Nat, v => Nat.double(v), U.U32Nat.dbl(p, Nat.double(x)), Nat.double(U.U32Nat.dbl(p, x)), ns.dbl_double(p, x))

Uses (4):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.dbl