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def ns.dkm

bend-osdev-word64@0.1.1.0 · proof_shift.bend:198

import bend-osdev-word64@0.1.1.0/proof_shift.bend as ProofShift
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

198# k <= n: 2^k * 2^(n - k) = 2^n, either way round
199def ns.dkm(+n: Nat, +k: Nat, +x: Nat, h: {Nat.is_le(k, n) == True{} : Bool}) -> {U.U32Nat.dbl(k, U.U32Nat.dbl(Nat.sub(n, k), x)) == U.U32Nat.dbl(n, x) : Nat}:
200  Equal.trans(Nat, U.U32Nat.dbl(k, U.U32Nat.dbl(Nat.sub(n, k), x)), U.U32Nat.dbl(Nat.add(k, Nat.sub(n, k)), x), U.U32Nat.dbl(n, x), UL.dbl_dbl(k, Nat.sub(n, k), x), Equal.cong(Nat, Nat, v => U.U32Nat.dbl(v, x), Nat.add(k, Nat.sub(n, k)), n, ns.add_sub_le(k, n, h)))

Uses (10)

Used by (6)