law gj

lawful-bytes@0.1.1.0 · proof_fast_append.bend:625

import Base
import lawful-bytes@0.1.1.0/proof_core.bend as C
import lawful-words@0.1.0.0/defs.bend as W
import lawful-arrays@0.1.0.0/defs.bend as A
import lawful-arrays@0.1.0.0/proof_tree.bend as P

625# Byte j of the window at 4 si + r, for j below m.
626law gj:
627  for +ts: P.Tree<U32>
628  for +e: Nat
629  for +si: U32
630  for +p: U32
631  for +lo: U32
632  for +r: Nat
633  for +m: Nat
634  for +j: Nat
635  for +hf: {A.full(U32, P.fromT(U32, ts), e) == True{} : Bool}
636  for +he: {Nat.is_le(e, 29n) == True{} : Bool}
637  for +hlo: {lo == C.WD(ts, si) : U32}
638  for +hp: {U32.to_nat(p) == Nat.add(U32.to_nat(si), 1n) : Nat}
639  for +hr: {Nat.is_lt(r, 4n) == True{} : Bool}
640  for +hm: {Nat.is_le(m, 4n) == True{} : Bool}
641  for +hb: {Nat.is_le(Nat.add(Nat.add(Nat.mul(U32.to_nat(si), 4n), r), m), Nat.mul(4n, Nat.pow(2n, e))) == True{} : Bool}
642  for +hjm: {Nat.is_lt(j, m) == True{} : Bool}
643  {List.get(&2, U32, List.drop(&2, U32, US(ts), Nat.add(Nat.mul(U32.to_nat(si), 4n), r)), j) == Some{W.byte(W.merge(lo, C.WD(ts, p), r), j)} : Maybe<&2, U32>}