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Proof step 25 from proof bitsand-app-zeros-01 (previous step)

bits1 = bits4 + boolvar0 ', ∀ bits0, bits, bits2. # bits2 < # bits1 → true → bits2 = [] ∨ sgn(bitsand(bits + false ' + bits0, bits2)) = sgn(bitsand(false ' + bits0, bits2)) ∨ true ∈ bits ⊦ bits1 = [], sgn(bitsand(bits + false ' + bits3 + boolvar ', bits1)) = sgn(bitsand(false ' + bits3, bits4) + (boolvar ∧ boolvar0)'), # bits1 = 1, true ∈ bits

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
∀ bits0, bits, bits2. # bits2 < #(bits4 + boolvar0 ') → true → bits2 = [] ∨ sgn(bitsand(bits + false ' + bits0, bits2)) = sgn(bitsand(false ' + bits0, bits2)) ∨ true ∈ bits ⊦ sgn(bitsand(bits + false ' + bits3 + boolvar ', bits4 + boolvar0 ')) = sgn(bitsand(false ' + bits3, bits4) + (boolvar ∧ boolvar0)'), bits4 = [], true ∈ bits

Rule argument

Additional information

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