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Proof step 83 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 84:
n = # fillsgn(n, mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1), sgn(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n ≤ # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), n0 + 1 + # bits1 < n, bits0.first, # bits0 ≤ 2 + # bits1, n0 + 1 + # bits1 < # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) ⊦ boolvar ↔ boolvar0, n0 = 0, lastn(n, bitsand(boolvar ' + boolvar0 ' + bits1, bits0)) = lastn(n, fillsgn(n, mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0))), bits0 = [], boolvar ∧ boolvar0

Rule argument

Additional information

Used simplifier rules: and-notempty-02: ⊦ bits0 ≠ [] → bitsand(boolvar ' + bits, bits0) ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)