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Proof step 25 from proof or-invandinv (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ bits0 ≠ [] ∧ bits = true ' → bitsand(bits, bits0) = bits0

Rule argument

name: and-rec-03 rotate: F subst: [bits0, bits] → [bitsinvert(bits0), true ']

Additional information

Used simplifier rules: ⊦ bitsinvert(bitsinvert(bits)) = bits;% ⊦ bitsinvert(bits) = [] ↔ bits = []; Used terms: bitsinvert(bits0), true '