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Proof step 90 from proof bitsand-cast (previous step)

# bits = 2 + # bits1, sgn(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n = # fillsgn(n, mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1), n0 + 1 + # bits1 < n ⊦ bits2 = [], lastn(n, fillsgn(n, bitsand(boolvar ' + boolvar0 ' + bits1, bits2 + bits))) = lastn(n, fillsgn(n, bitsand(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1, bits2 + bits))), n0 = 0, boolvar ↔ boolvar0, bits2 + bits = [], boolvar ∧ boolvar0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 91:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)
Proof step 92:
boolvar ' + boolvar0 ' + bits1 ≠ [] ∧ bits2 + bits ≠ [], # bits = 2 + # bits1, sgn(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n = # fillsgn(n, mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1), n0 + 1 + # bits1 < n ⊦ bits2 = [], lastn(n, fillsgn(n, bitsand(bits2 + bits, boolvar ' + boolvar0 ' + bits1))) = lastn(n, fillsgn(n, bitsand(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1, bits2 + bits))), n0 = 0, boolvar ↔ boolvar0, bits2 + bits = [], boolvar ∧ boolvar0

Rule argument

name: and-com rotate: F subst: [bits0, bits] → [bits2 + bits, boolvar ' + boolvar0 ' + bits1]

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bits2 + bits, boolvar ' + boolvar0 ' + bits1