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Proof step 842 from proof bitsand-cast (previous step)

2 + # bits + m ≤ #((bits2 + mklist(boolvar, m)) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)), sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits, bits0.first, # bits0 ≤ 2 + # bits ⊦ bits0 = [], boolvar ↔ boolvar0, lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(2 + # bits + m, (bits2 + mklist(boolvar, m)) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)), boolvar ∧ boolvar0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 843:
sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits, bits0.first, # bits0 ≤ 2 + # bits, 2 + # bits ≤ # bits2 + # bitsand(boolvar ' + boolvar0 ' + bits, bits0), # bits0 ≤ # bits2 + # bitsand(boolvar ' + boolvar0 ' + bits, bits0) ⊦ bits0 = [], boolvar ↔ boolvar0, lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(2 + # bits + m, (bits2 + mklist(boolvar, m)) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)), boolvar ∧ boolvar0

Rule argument

Additional information

Used simplifier rules: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;