def wsd.sd3b

bend-osdev-word64@0.1.1.0 · PROOF_text.bend:316

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

316def wsd.sd3b(+hh: U32, +ll: U32, +a1: {U32.to_nat(wsd.q(0, 0, U32.shrn(hh, 16n))) == Nat.add(U.U32Nat.dbl(16n, U32.to_nat(0)), U32.to_nat(wsd.d(0, U32.shrn(hh, 16n)))) : Nat}, +a2: {U32.to_nat(wsd.q(wsd.q(0, 0, U32.shrn(hh, 16n)), wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535))) == Nat.add(U.U32Nat.dbl(16n, U32.to_nat(wsd.q(0, 0, U32.shrn(hh, 16n)))), U32.to_nat(wsd.d(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)))) : Nat}, +b1: {Nat.add(Nat.mul(U32.to_nat(wsd.d(0, U32.shrn(hh, 16n))), 10n), U32.to_nat(wsd.m(0, U32.shrn(hh, 16n)))) == Nat.add(U.U32Nat.dbl(16n, U32.to_nat(0)), U32.to_nat(U32.shrn(hh, 16n))) : Nat}, +b2: {Nat.add(Nat.mul(U32.to_nat(wsd.d(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535))), 10n), U32.to_nat(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)))) == Nat.add(U.U32Nat.dbl(16n, U32.to_nat(wsd.m(0, U32.shrn(hh, 16n)))), U32.to_nat(U32.and(hh, 65535))) : Nat}, +a3: {U32.to_nat(wsd.q(0, wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))) == Nat.add(U.U32Nat.dbl(16n, U32.to_nat(0)), U32.to_nat(wsd.d(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n)))) : Nat}, +b3: {Nat.add(Nat.mul(U32.to_nat(wsd.d(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))), 10n), U32.to_nat(wsd.m(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n)))) == Nat.add(U.U32Nat.dbl(16n, U32.to_nat(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)))), U32.to_nat(U32.shrn(ll, 16n))) : Nat}, +m3: {Nat.is_lt(U32.to_nat(wsd.m(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))), 10n) == True{} : Bool}, +d3: {Nat.is_lt(U32.to_nat(wsd.d(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))), U.U32Nat.dbl(16n, 1n)) == True{} : Bool}) -> {Nat.add(Nat.mul(W.W64.to_nat(W.W64.small.q(W.W64.small.divmod(W.W64{hh, ll}, 10))), 10n), U32.to_nat(W.W64.small.r(W.W64.small.divmod(W.W64{hh, ll}, 10)))) == W.W64.to_nat(W.W64{hh, ll}) : Nat} & {Nat.is_lt(U32.to_nat(W.W64.small.r(W.W64.small.divmod(W.W64{hh, ll}, 10))), 10n) == True{} : Bool}:
317  wsd.sd4(hh, ll, a1, a2, a3, b1, b2, b3, wsd.step(wsd.m(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n)), wsd.q(0, wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n)), U32.and(ll, 65535), m3, Equal.trans(Bool, Nat.is_lt(U32.to_nat(U32.and(ll, 65535)), U.U32Nat.dbl(16n, 1n)), Nat.is_lt(U.U32Nat.low(16n, U32.to_nat(ll)), U.U32Nat.dbl(16n, 1n)), True{}, Equal.cong(Nat, Bool, zz => Nat.is_lt(zz, U.U32Nat.dbl(16n, 1n)), U32.to_nat(U32.and(ll, 65535)), U.U32Nat.low(16n, U32.to_nat(ll)), Equal.sym(Nat, U.U32Nat.low(16n, U32.to_nat(ll)), U32.to_nat(U32.and(ll, 65535)), Equal.sym(Nat, U32.to_nat(U32.and(ll, 65535)), U.U32Nat.low(16n, U32.to_nat(ll)), UL.u32_and_65535(ll)))), UL.low_lt(16n, U32.to_nat(ll))), Equal.trans(Bool, Nat.is_lt(U32.to_nat(wsd.q(0, wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))), U.U32Nat.dbl(16n, 1n)), Nat.is_lt(U32.to_nat(wsd.d(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))), U.U32Nat.dbl(16n, 1n)), True{}, Equal.cong(Nat, Bool, zz => Nat.is_lt(zz, U.U32Nat.dbl(16n, 1n)), U32.to_nat(wsd.q(0, wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))), U32.to_nat(wsd.d(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))), Equal.sym(Nat, U32.to_nat(wsd.d(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))), U32.to_nat(wsd.q(0, wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))), Equal.sym(Nat, U32.to_nat(wsd.q(0, wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))), U32.to_nat(wsd.d(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))), Equal.trans(Nat, U32.to_nat(wsd.q(0, wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))), Nat.add(U.U32Nat.dbl(16n, U32.to_nat(0)), U32.to_nat(wsd.d(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n)))), U32.to_nat(wsd.d(wsd.m(wsd.m(0, U32.shrn(hh, 16n)), U32.and(hh, 65535)), U32.shrn(ll, 16n))), a3, {==})))), d3)))