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Proof step 6 from proof bitsand-cast-05 (previous step)

¬(#(false ' + bits1) ≤ n ∧ ¬ (false ' + bits1).first ∧ bits ≠ [] ∧ false ' + bits1 ≠ []), # bits1 ≤ n ⊦ bits = [], n = 0, sgn(bitsand(lastn(n, fillsgn(n, bits)), false ' + bits1)) = sgn(bitsand(bits, false ' + bits1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
⊦ bits = [], sgn(bitsand(lastn(# bits1, fillsgn(# bits1, bits)), false ' + bits1)) = sgn(bitsand(bits, false ' + bits1)), bits1 = []

Rule argument

Additional information

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