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Proof step 3 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))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsor(bits, bits0) = bitsor(bits.butlast, bits0.butlast) + (bits.last ∨ bits0.last)
Proof step 5:
¬(1 < # bits ∧ 1 < # bits0), ∀ 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))
Proof step 26:
1 < # bits ∧ 1 < # bits0, ∀ 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.butlast, bits0.butlast) + (bits.last ∨ bits0.last))

Rule argument

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

Additional information

Used terms: bits0, bits