law fi

lawful-bytes@0.1.1.0 · proof_fast_find.bend:706

import Base
import lawful-bytes@0.1.1.0/defs.bend as D
import lawful-bytes@0.1.1.0/fast.bend as FA
import lawful-bytes@0.1.1.0/proof_core.bend as C
import lawful-bytes@0.1.1.0/proof_fast_word.bend as FW
import lawful-arrays@0.1.0.0/proof_tree.bend as P

706# The loop invariant, for 1 + k words left (wi's included): the answer, capped
707# at to, is the first c from the start o bytes into word wi.
708law fi:
709  for +k: Nat
710  for +z: Bool
711  for +len: U32
712  for +t: P.Tree<U32>
713  for +d: Nat
714  for +to: U32
715  for +c: U32
716  for +wi: U32
717  for +o: Nat
718  for +v: U32
719  for +h: {D.ok(C.BT(len, t), d) == True{} : Bool}
720  for +ht: {Nat.is_le(U32.to_nat(to), U32.to_nat(len)) == True{} : Bool}
721  for +hc: {U32.is_lt(c, 256) == True{} : Bool}
722  for +ho: {Nat.is_lt(o, 4n) == True{} : Bool}
723  for +hs: {Nat.is_le(SS(wi, o), U32.to_nat(to)) == True{} : Bool}
724  for +he1: {Nat.is_le(U32.to_nat(to), Nat.mul(Nat.add(U32.to_nat(wi), 1n+k), 4n)) == True{} : Bool}
725  for +he2: {Nat.is_lt(Nat.mul(Nat.add(U32.to_nat(wi), k), 4n), U32.to_nat(to)) == True{} : Bool}
726  for +hv: {FW.P0(v) == Nat.add(o, D.run_len(AW(t, wi, o), c)) : Nat}
727  for +hz: {U32.is_zero(FA.zb(v)) == z : Bool}
728  {U32.to_nat(U32.min(FG(1n+k, z, wi, FA.zb(v), FA.rep(c), t), to)) == D.first(UB(t), SS(wi, o), U32.to_nat(to), c) : Nat}