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Proof step 15 from proof bitsor-bi-sgn (previous step)

∀ bits, bits1. # bits1 < # bits0 → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bits0 = true ', bits0 = false ', # bits0 = 1, bits0 = [], bits2int(bitsor(true ', bits0)) = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ bits0 ≠ [] ∧ bits = false ' → bitsor(bits, bits0) = bits0
Proof step 17:
¬(bits0 ≠ [] ∧ true ' = false '), ∀ bits, bits1. # bits1 < # bits0 → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bits0 = true ', bits0 = false ', # bits0 = 1, bits0 = [], bits2int(bitsor(true ', bits0)) = ~1

Rule argument

name: or-rec-04 rotate: F subst: [bits0, bits] → [bits0, true ']

Additional information

Used simplifier rules: ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0; Used terms: bits0, true '