def limbs_take

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/bounds.bend:86

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/spec/crypto/secp256k1/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as Lg

86# the first j limbs of a list whose first n >= j limbs are fine
87def limbs_take(+one: Nat, n: Nat, j: Nat, +xs: List<&2, Nat>, +hj: {Nat.is_le(j, n) == True{} : Bool}, +h: {FS.limbs16(one, n, L.take(n, xs)) == True{} : Bool}) -> {FS.limbs16(one, j, L.take(j, xs)) == True{} : Bool}:
88  match n j xs:
89    case 0n 0n _:
90      {==}
91    case 0n 1n+i _:
92      Empty.absurd({FS.limbs16(one, 1n+i, L.take(1n+i, xs)) == True{} : Bool}, Lg.false_true(hj))
93    case 1n+k 0n _:
94      {==}
95    case 1n+k 1n+i Nil{}:
96      Empty.absurd({FS.limbs16(one, 1n+i, L.take(1n+i, [])) == True{} : Bool}, Lg.false_true(h))
97    case 1n+ +k 1n+ +i +x <> +t:
98      +hx = Lg.and_left(Nat.is_lt(x, C.shift(16n, one)), FS.limbs16(one, k, L.take(k, t)), h)
99      +ht = Lg.and_right(Nat.is_lt(x, C.shift(16n, one)), FS.limbs16(one, k, L.take(k, t)), h)
100      Lg.and_intro(Nat.is_lt(x, C.shift(16n, one)), FS.limbs16(one, i, L.take(i, t)), hx, limbs_take(one, k, i, t, hj, ht))