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Proof step 13 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 = [], bits0 = true ', bits0 = false ', bits ≠ bits.first ' ∧ bits0 ≠ bits0.first '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ bits0 ≠ [] ∧ bits = true ' → bitsor(bits, bits0) = true '
Proof step 15:
¬(bits0 ≠ [] ∧ bits = true '), ∀ 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 = [], bits0 = true ', bits0 = false ', bits ≠ bits.first ' ∧ bits0 ≠ bits0.first '
Proof step 27:
bits0 ≠ [] ∧ bits = true ', ∀ bits1, bits0. # bits1 < # bits → true → bits1 = [] ∨ bits0 = [] ∨ bitsor(bits1, bits0) = bitsinvert(bitsand(bitsinvert(bits1), bitsinvert(bits0))) ⊦ true ' = bitsinvert(bitsand(bitsinvert(bits), bitsinvert(bits0))), bits0 = [], bits = [], bits0 = true ', bits0 = false ', bits ≠ bits.first ' ∧ bits0 ≠ bits0.first '

Rule argument

name: or-rec-03 rotate: F subst: [bits0, bits] → [bits0, bits]

Additional information

Used terms: bits0, bits