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Proof step 179 from proof bitsand-cast (previous step)

# bits = 2 + # bits1, n = # fillsgn(n, false ' + true ' + bits1), # bits < n ⊦ bits2 + bits = [], bits2 = [], lastn(n, fillsgn(n, bitsand(bits, false ' + true ' + bits1))) = lastn(n, fillsgn(n, bitsand(false ' + true ' + bits1, bits2 + bits)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 180:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)
Proof step 181:
false ' + true ' + bits1 ≠ [] ∧ bits2 + bits ≠ [], # bits = 2 + # bits1, n = # fillsgn(n, false ' + true ' + bits1), # bits < n ⊦ bits2 + bits = [], bits2 = [], lastn(n, fillsgn(n, bitsand(bits, false ' + true ' + bits1))) = lastn(n, fillsgn(n, bitsand(bits2 + bits, false ' + true ' + bits1)))

Rule argument

name: and-com rotate: F subst: [bits0, bits] → [bits2 + bits, false ' + true ' + bits1]

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bits2 + bits, false ' + true ' + bits1