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Proof step 19 from proof bitsand-app-zeros (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ bits ≠ [] ∧ bits0 = false ' → bitsand(bits, bits0) = false '

Rule argument

name: and-rec-02 rotate: F subst: [bits0, bits] → [false ', bits + false ' + bits0]

Additional information

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