def bytes_le_v

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/bytes.bend:269

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/spec/crypto/secp256k1/curve.bend as CV
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/bytes.bend as B
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as Lg
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as LV

269def bytes_le_v(+one: Nat, +h1: {one == 1n : Nat}, k: Nat, xs: List<&2, Nat>, +h: {FS.limbs16(one, k, xs) == True{} : Bool}) -> {B.bytes_le(xs) == CV.i2osp_le(Nat.double(k), LV.ev(xs)) : List<&2, U32>}:
270  match k xs:
271    case 0n Nil{}:
272      {==}
273    case 0n x <> t:
274      Empty.absurd({B.bytes_le(x <> t) == CV.i2osp_le(Nat.double(0n), LV.ev(x <> t)) : List<&2, U32>}, Lg.false_true(h))
275    case 1n+j Nil{}:
276      Empty.absurd({B.bytes_le([]) == CV.i2osp_le(Nat.double(1n+j), LV.ev([])) : List<&2, U32>}, Lg.false_true(h))
277    case 1n+ +j +x <> +t:
278      +hx = Lg.and_left(Nat.is_lt(x, C.shift(16n, one)), FS.limbs16(one, j, t), h)
279      +ht = Lg.and_right(Nat.is_lt(x, C.shift(16n, one)), FS.limbs16(one, j, t), h)
280      +f16 = fits_one(16n, one, h1, x, hx)
281      +v = Nat.add(x, C.shift(16n, LV.ev(t)))
282      +e1 = low_v(x, LV.ev(t))
283      +e2 = mid_v(x, LV.ev(t), f16)
284      +e3 = top_v(x, LV.ev(t), f16)
285      %Equal.sym(Nat, C.low(8n, Nat.add(x, C.shift(16n, LV.ev(t)))), Nat.mod(x, 256n), e1) : {U32.from_nat(Nat.mod(x, 256n)) <> U32.from_nat(Nat.div(x, 256n)) <> B.bytes_le(t) == U32.from_nat(_) <> U32.from_nat(C.low(8n, C.high(8n, Nat.add(x, C.shift(16n, LV.ev(t)))))) <> CV.i2osp_le(Nat.double(j), C.high(8n, C.high(8n, Nat.add(x, C.shift(16n, LV.ev(t)))))) : List<&2, U32>}
286      %Equal.sym(Nat, C.low(8n, C.high(8n, Nat.add(x, C.shift(16n, LV.ev(t))))), Nat.div(x, 256n), e2) : {U32.from_nat(Nat.mod(x, 256n)) <> U32.from_nat(Nat.div(x, 256n)) <> B.bytes_le(t) == U32.from_nat(Nat.mod(x, 256n)) <> U32.from_nat(_) <> CV.i2osp_le(Nat.double(j), C.high(8n, C.high(8n, Nat.add(x, C.shift(16n, LV.ev(t)))))) : List<&2, U32>}
287      %Equal.sym(Nat, C.high(8n, C.high(8n, Nat.add(x, C.shift(16n, LV.ev(t))))), LV.ev(t), e3) : {U32.from_nat(Nat.mod(x, 256n)) <> U32.from_nat(Nat.div(x, 256n)) <> B.bytes_le(t) == U32.from_nat(Nat.mod(x, 256n)) <> U32.from_nat(Nat.div(x, 256n)) <> CV.i2osp_le(Nat.double(j), _) : List<&2, U32>}
288      %Equal.sym(List<&2, U32>, B.bytes_le(t), CV.i2osp_le(Nat.double(j), LV.ev(t)), bytes_le_v(one, h1, j, t, ht)) : {U32.from_nat(Nat.mod(x, 256n)) <> U32.from_nat(Nat.div(x, 256n)) <> _ == U32.from_nat(Nat.mod(x, 256n)) <> U32.from_nat(Nat.div(x, 256n)) <> CV.i2osp_le(Nat.double(j), LV.ev(t)) : List<&2, U32>}
289      {==}