def pos_add

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/limbs.bend:110

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

110def pos_add(n: Nat, +x: Nat, +y: Nat) -> {pos(n, Nat.add(x, y)) == Nat.add(pos(n, x), pos(n, y)) : Nat}:
111  match n:
112    case 0n:
113      {==}
114    case 1n+ +k:
115      %Equal.sym(Nat, pos(k, Nat.add(x, y)), Nat.add(pos(k, x), pos(k, y)), pos_add(k, x, y)) : {C.shift(16n, _) == Nat.add(C.shift(16n, pos(k, x)), C.shift(16n, pos(k, y))) : Nat}
116      %Equal.sym(Nat, C.shift(16n, Nat.add(pos(k, x), pos(k, y))), Nat.add(C.shift(16n, pos(k, x)), C.shift(16n, pos(k, y))), WW.shift_add(16n, pos(k, x), pos(k, y))) : {_ == Nat.add(C.shift(16n, pos(k, x)), C.shift(16n, pos(k, y))) : Nat}
117      {==}