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Proof step 43 from proof bitsand-cast-04 (previous step)

# bits1 ≤ # bits0 + n0, # bits0 < # bits1 ⊦ sgn(bitsand(false ' + bits0, false ' + bits1)) = sgn(bitsand(bits1, false ' + bits0)), n0 = 0, bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)
Proof step 45:
false ' + bits0 ≠ [] ∧ false ' + bits1 ≠ [], # bits1 ≤ # bits0 + n0, # bits0 < # bits1 ⊦ sgn(bitsand(false ' + bits1, false ' + bits0)) = sgn(bitsand(bits1, false ' + bits0)), n0 = 0, bits1 = []

Rule argument

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

Additional information

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