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Proof step 3 from proof sgn-length (previous step)

# bits0 < # sgn(bits0) → sgn(bits0) = [] ⊦ #(boolvar + bits0) < # sgn(boolvar + bits0) → sgn(boolvar + bits0) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
1 + # bits0 < # sgn(boolvar ' + bits0), ¬ # sgn(bits0) ≤ # bits0 → sgn(bits0) = [] ⊦

Rule argument

Additional information

Used simplifier rules: sgn-not-empty-01: ⊦ sgn(boolvar ' + bits) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar + bits = boolvar ' + bits;