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Proof step 34 from proof bitsand-app-zeros-01 (previous step)

true ∈ bitsand(false ' + bits3, bits4), ∀ bits0, bits, bits2. # bits2 < #(bits4 + boolvar0 ') → true → bits2 = [] ∨ sgn(bitsand(bits + false ' + bits0, bits2)) = sgn(bitsand(false ' + bits0, bits2)) ∨ true ∈ bits ⊦ sgn(bitsand(bits + false ' + bits3, bits4) + (boolvar ∧ boolvar0)') = sgn(bitsand(false ' + bits3, bits4) + (boolvar ∧ boolvar0)'), bits4 = [], true ∈ bits, false ∈ bitsand(false ' + bits3, bits4)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ bits ≠ [] ∧ bits0 ≠ [] → (false ∈ bitsand(bits, bits0) ↔ false ∈ bits ∨ false ∈ bits0)

Rule argument

name: bitsand-zero-in rotate: F subst: [bits0, bits] → [bits4, false ' + bits3]

Additional information

Used simplifier rules: ⊦ boolvar ' ≠ [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' + bits ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;%⊦ ¬ boolvar ∈ boolvar0 ' + bits ↔ ¬(boolvar ↔ boolvar0) ∧ ¬ boolvar ∈ bits; Used terms: bits4, false ' + bits3