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Proof step 41 from proof or-invandinv (previous step)

∀ bits1, bits0. # bits1 < #(bits2 + boolvar ') → true → bits1 = [] ∨ bits0 = [] ∨ bitsor(bits1, bits0) = bitsinvert(bitsand(bitsinvert(bits1), bitsinvert(bits0))) ⊦ bits2 + boolvar ' = (bits2 + boolvar ').first ', bits + boolvar0 ' = (bits + boolvar0 ').first ', bitsor(bits2, bits) + (boolvar ∨ boolvar0)' = bitsinvert(bitsand(bitsinvert(bits2) + (¬ boolvar)', bitsinvert(bits) + (¬ boolvar0)'))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: and-rec rotate: F subst: [bits0, bits] → [bitsinvert(bits) + (¬ boolvar0)', bitsinvert(bits2) + (¬ boolvar)']

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # bitsinvert(bits) = # bits;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ m + 1 ≠ 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ 1 = m + 1 ↔ m = 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first);% ⊦ bitsinvert([]) = [];% ⊦ [] + bits = bits;% ⊦ boolvar '.first ↔ boolvar;% ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0; Used terms: bitsinvert(bits) + (¬ boolvar0)', bitsinvert(bits2) + (¬ boolvar)'