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Proof step 9 from proof bitsor-bi-sgn (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ bits ≠ [] ∧ bits0 = false ' → bitsor(bits, bits0) = bits
Proof step 11:
¬(bits ≠ [] ∧ bits0 = false '), ∀ bits, bits1. # bits1 < # bits0 → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bits = [], bits0 = [], bits2int(bitsor(sgn(bits), bits0)) = bits2int(bitsor(bits, bits0)), bits0 = true ', # bits ≠ 1 ∧ # bits0 ≠ 1
Proof step 20:
bits ≠ [] ∧ bits0 = false ', ∀ bits, bits1. # bits1 < # bits0 → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bits = [], bits0 = [], bits2int(bitsor(sgn(bits), bits0)) = bits2int(bits), bits0 = true ', # bits ≠ 1 ∧ # bits0 ≠ 1

Rule argument

name: or-rec-02 rotate: F subst: [bits0, bits] → [bits0, bits]

Additional information

Used terms: bits0, bits