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Proof step 48 from proof bitsand-cast-05 (previous step)

¬(# bits ≤ # bits1 ∧ bits ≠ [] ∧ ¬ bits.first), # bits = # bits1 ⊦ bits1 = [], sgn(bitsand(false ' + bits1, bits)) = sgn(false ' + bitsand(bits, bits1)), bits = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
# bits = # bits1, bits.first ⊦ sgn(false ' + bitsand(bits1, bits)) = sgn(false ' + bitsand(bits, bits1)), bits1 = [], bits = []

Rule argument

Additional information

Used simplifier rules: bitsand-app-true: ⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ bits1.first → bitsand(bits + bits0, bits1) = bits + bitsand(bits0, bits1);% ⊦ m ≤ m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ ¬ n < n;% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ ¬ m ≤ n ↔ n < m;