def bit_lo

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/bitsrel.bend:91

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend as WW

91# below 16: the bits of the limb (j + 1 + d = 16)
92def bit_lo(+j: Nat, +d: Nat, +x: Nat, +r: Nat) -> {C.bit(C.high(j, Nat.add(x, C.shift(Nat.add(j, 1n+d), r)))) == C.bit(C.high(j, x)) : Nat}:
93  %Equal.sym(Nat, C.shift(Nat.add(j, 1n+d), r), C.shift(j, C.shift(1n+d, r)), WW.shift_comp(j, 1n+d, r)) : {C.bit(C.high(j, Nat.add(x, _))) == C.bit(C.high(j, x)) : Nat}
94  %Equal.sym(Nat, C.high(j, Nat.add(x, C.shift(j, C.shift(1n+d, r)))), Nat.add(C.high(j, x), C.shift(1n+d, r)), WW.high_add_shift(j, x, C.shift(1n+d, r))) : {C.bit(_) == C.bit(C.high(j, x)) : Nat}
95  WW.bit_dbl(C.high(j, x), C.shift(d, r))