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Proof step 13 from proof bitsand-app-zeros-01 (previous step)

∀ bits0, bits, bits2. # bits2 < # bits1 → true → bits2 = [] ∨ sgn(bitsand(bits + false ' + bits0, bits2)) = sgn(bitsand(false ' + bits0, bits2)) ∨ true ∈ bits ⊦ # bits1 = 1, bits1 = false ', bits1 = true ', bits1 = [], sgn(bitsand(bits + false ', bits1)) = false ', true ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ ¬ true ∈ bits ∧ bits ≠ [] ∧ bits0 ≠ [] → sgn(bitsand(bits, bits0)) = false '

Rule argument

name: bitsand-zeros-02 rotate: F subst: [bits0, bits] → [bits1, bits + false ']

Additional information

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