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Proof step 34 from proof bitsand-cast-05 (previous step)

#(false ' + bits1) ≤ # bits0 ∧ false ' + bits1 ≠ [] ∧ ¬ (false ' + bits1).first, # bits0 = 1 + # bits1, # bits1 < # bits2 + # bits0 ⊦ # bits1 = # bits2 + # bits0, bits2 + bits0 = [], sgn(bitsand(lastn(# bits1, bits2 + bits0), false ' + bits1)) = sgn(bitsand(bits0, false ' + bits1)), bits1 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
# bits0 = 1 + # bits1, # bits1 < # bits0, # bits1 < # bits2 + # bits0 ⊦ bits1 = [], sgn(bitsand(lastn(# bits1, bits2 + bits0), false ' + bits1)) = sgn(bitsand(bits0, false ' + bits1)), bits2 + bits0 = [], # bits1 = # bits2 + # bits0, bits0 = []

Rule argument

Additional information

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