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Proof step 4 from proof or-invandinv (previous step)

∀ bits1, bits0. # bits1 < # bits → true → bits1 = [] ∨ bits0 = [] ∨ bitsor(bits1, bits0) = bitsinvert(bitsand(bitsinvert(bits1), bitsinvert(bits0))) ⊦ bitsor(bits, bits0) = bitsinvert(bitsand(bitsinvert(bits), bitsinvert(bits0))), bits0 = [], bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsor(bits, bits0) = bitsor(bits.butlast, bits0.butlast) + (bits.last ∨ bits0.last)
Proof step 6:
¬(1 < # bits ∧ 1 < # bits0), ∀ bits1, bits0. # bits1 < # bits → true → bits1 = [] ∨ bits0 = [] ∨ bitsor(bits1, bits0) = bitsinvert(bitsand(bitsinvert(bits1), bitsinvert(bits0))) ⊦ bitsor(bits, bits0) = bitsinvert(bitsand(bitsinvert(bits), bitsinvert(bits0))), bits0 = [], bits = []
Proof step 36:
1 < # bits ∧ 1 < # bits0, ∀ bits1, bits0. # bits1 < # bits → true → bits1 = [] ∨ bits0 = [] ∨ bitsor(bits1, bits0) = bitsinvert(bitsand(bitsinvert(bits1), bitsinvert(bits0))) ⊦ bitsor(bits.butlast, bits0.butlast) + (bits.last ∨ bits0.last) = bitsinvert(bitsand(bitsinvert(bits), bitsinvert(bits0))), bits0 = [], bits = []

Rule argument

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

Additional information

Used terms: bits0, bits