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Proof step 51 from proof bitsand-cast-05 (previous step)

1 + # bits0 = # bits1 ⊦ bits1 = [], sgn(false ' + bitsand(bits1, true ' + bits0)) = sgn(false ' + bitsand(true ' + bits0, bits1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 52:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)

Rule argument

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

Additional information

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