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Proof step 49 from proof bitsand-cast (previous step)

boolvar ' + boolvar0 ' + bits1 ≠ [] ∧ bits0 ≠ [], sgn(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n = # fillsgn(n, mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1), n = # fillsgn(n, mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)), # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n, # bits0 ≤ 2 + # bits1, bits0.first, n0 + 1 + # bits1 < n, (n0 - 1) + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n ⊦ bits0 = [], mklist((boolvar ' + boolvar0 ' + bits1).first ∧ bits0.first, n - # bitsand(boolvar ' + boolvar0 ' + bits1, bits0)) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0) = fillsgn(n, mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)), n0 = 0, boolvar ↔ boolvar0, boolvar ∧ boolvar0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
sgn(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n = # fillsgn(n, mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1), n = # fillsgn(n, mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)), # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n, # bits0 ≤ 2 + # bits1, bits0.first, n0 + 1 + # bits1 < n, (n0 - 1) + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n ⊦ n0 = 0, boolvar ↔ boolvar0, bits0 = [], mklist(boolvar, n - # bitsand(boolvar ' + boolvar0 ' + bits1, bits0)) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0) = fillsgn(n, mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)), boolvar ∧ boolvar0

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ' + bits ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (boolvar ' + bits).first ↔ boolvar;