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Proof step 376 from proof bitsand-cast (previous step)

sgn(mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits ⊦ boolvar ↔ boolvar0, bits0 = [], n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits2 + mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits, bits0))), boolvar ∧ boolvar0

User applied rule cut formula

And obtained the following new goals

Proof step 377:
bits2 + mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits = (bits2 + mklist(boolvar, n - 1)) + boolvar ' + boolvar0 ' + bits, sgn(mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits ⊦ boolvar ↔ boolvar0, bits0 = [], n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits2 + mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits, bits0))), boolvar ∧ boolvar0

Rule argument

fma: bits2 + mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits = (bits2 + mklist(boolvar, n - 1)) + boolvar ' + boolvar0 ' + bits

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used formulas: bits2 + mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits = (bits2 + mklist(boolvar, n - 1)) + boolvar ' + boolvar0 ' + bits