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Proof step 9 from proof bitsand-app-ones (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ bits ≠ [] ∧ bits0 = false ' → bitsand(bits, bits0) = false '
Proof step 11:
true ' + bits0 ≠ [] ∧ false ' = false ', ∀ bits0, bits, bits2. # bits2 < # [] → true → bitsand(bits + true ' + bits0, false ' + bits2) = bitsand(true ' + bits0, false ' + bits2) ∨ false ∈ bits ⊦ bits0 = [], bitsand(bits + true ' + bits0, false ') = false ', false ∈ bits

Rule argument

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

Additional information

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