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Proof step 19 from proof bitsand-app-zeros-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: and-rec-01 rotate: F subst: [bits0, bits] → [true ', bits + false ' + bits0]

Additional information

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