def take_okb

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/poly.bend:339

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM

339def take_okb(+n: Nat, +xs: List<&2, U32>, +b: Nat, +hl: {len_ge(n, xs) == True{} : Bool}, +hx: {LM.lea(xs, b) == True{} : Bool}) -> {LM.okb(n, F.take(n, xs), b) == True{} : Bool}:
340  match n xs:
341    case 0n _:
342      {==}
343    case 1n+m Nil{}:
344      Empty.absurd({LM.okb(1n+m, Nil{}, b) == True{} : Bool}, L.false_true(hl))
345    case 1n+ +m Con{+x, +xt}:
346      L.and_intro(Nat.is_le(v(x), b), LM.okb(m, F.take(m, xt), b), LM.lea_head(x, xt, b, hx), take_okb(m, xt, b, hl, LM.lea_tail(x, xt, b, hx)))