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Proof step 48 from proof bitsand-app-zeros (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) ≠ []

Rule argument

name: and-notempty rotate: F subst: [bits0, bits] → [false ' + bits4, bits + false ' + bits3]

Additional information

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