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Proof step 388 from proof bitsand-cast (previous step)

# bits1 = 2 + # bits, sgn(mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits ⊦ bits3 = [], lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(boolvar ' + boolvar0 ' + bits, bits3 + bits1))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(boolvar, n - 1)) + boolvar ' + boolvar0 ' + bits, bits3 + bits1))), n = 0, bits3 + bits1 = [], boolvar ↔ boolvar0, boolvar ∧ boolvar0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 389:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)
Proof step 390:
boolvar ' + boolvar0 ' + bits ≠ [] ∧ bits3 + bits1 ≠ [], # bits1 = 2 + # bits, sgn(mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits ⊦ bits3 = [], lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits3 + bits1, boolvar ' + boolvar0 ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(boolvar, n - 1)) + boolvar ' + boolvar0 ' + bits, bits3 + bits1))), n = 0, bits3 + bits1 = [], boolvar ↔ boolvar0, boolvar ∧ boolvar0

Rule argument

name: and-com rotate: F subst: [bits0, bits] → [bits3 + bits1, boolvar ' + boolvar0 ' + bits]

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bits3 + bits1, boolvar ' + boolvar0 ' + bits