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Proof step 39 from proof bitsand-cast-05 (previous step)

bits0 = boolvar + bits, # bits0 = 1 + # bits1, # bits1 < # bits0, # bits1 < # bits2 + # bits0 ⊦ bits2 + bits0 = [], # bits1 = # bits2 + # bits0, bits0 = [], bits1 = [], sgn(bitsand(bits, false ' + bits1)) = sgn(bitsand(bits0, false ' + bits1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
# bits = # bits1 ⊦ sgn(bitsand(bits, false ' + bits1)) = sgn(bitsand(boolvar ' + bits, false ' + bits1)), bits1 = []

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m;% ⊦ m ≤ m + n;% ⊦ m + 1 ≠ 0;% ⊦ m = m + n ↔ n = 0;% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ boolvar ' + bits ≠ [];% ⊦ bits + boolvar ' + bits0 ≠ [];% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ boolvar + bits = boolvar ' + bits;