def allred_app

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/point.bend:106

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as Lg

106def allred_app(+one: Nat, rs: List<&2, List<&2, Nat>>, +x: List<&2, Nat>, +h: {allred(one, rs) == True{} : Bool}, +hx: {red(one, x) == True{} : Bool}) -> {allred(one, List.append(&2, List<&2, Nat>, rs, [x])) == True{} : Bool}:
107  match rs:
108    case Nil{}:
109      Lg.and_intro(red(one, x), True{}, hx, {==})
110    case +r <> +t:
111      Lg.and_intro(red(one, r), allred(one, List.append(&2, List<&2, Nat>, t, [x])), Lg.and_left(red(one, r), allred(one, t), h), allred_app(one, t, x, Lg.and_right(red(one, r), allred(one, t), h), hx))