law p0_low2

lawful-bytes@0.1.1.0 · proof_fast_find2.bend:165

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

165# The first word of a search, for two values.
166law p0_low2:
167  for +w: U32
168  for +c1: U32
169  for +c2: U32
170  for +i: U32
171  for +hc1: {U32.is_lt(c1, 256) == True{} : Bool}
172  for +hc2: {U32.is_lt(c2, 256) == True{} : Bool}
173  {Nat.min(FW.P0(U32.or(U32.xor(w, FA.rep(c1)), U32.not(FA.low(i)))), FW.P0(U32.or(U32.xor(w, FA.rep(c2)), U32.not(FA.low(i))))) == Nat.add(U32.to_nat((i .&. 3 : U32)), D.run_len2(List.drop(&2, U32, C.L4(w), U32.to_nat((i .&. 3 : U32))), c1, c2)) : Nat}