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Proof step 7 from proof bitsand-app-zeros (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ bits ≠ [] ∧ bits0 = true ' → bitsand(bits, bits0) = bits
Proof step 9:
¬(false ' + bits0 ≠ [] ∧ false ' + bits1 = true '), ∀ bits0, bits, bits2. # bits2 < # bits1 → true → sgn(bitsand(bits + false ' + bits0, false ' + bits2)) = sgn(bitsand(false ' + bits0, false ' + bits2)) ∨ true ∈ bits ⊦ sgn(bitsand(bits + false ' + bits0, false ' + bits1)) = sgn(bitsand(false ' + bits0, false ' + bits1)), true ∈ bits, bits0 ≠ [] ∧ bits1 ≠ []

Rule argument

name: and-rec-01 rotate: F subst: [bits0, bits] → [false ' + bits1, false ' + bits0]

Additional information

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