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Proof step 39 from proof bitsand-cast-04 (previous step)

#(false ' + bits0) ≤ # bits1 ∧ false ' + bits0 ≠ [] ∧ ¬ (false ' + bits0).first, # bits0 < # bits1, # bits1 ≤ # bits0 + n0 ⊦ sgn(bitsand(mklist(false, n0) + false ' + bits0, false ' + bits1)) = sgn(bitsand(bits1, false ' + bits0)), n0 = 0, bits1 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
# bits1 ≤ # bits0 + n0, # bits0 < # bits1 ⊦ sgn(bitsand(mklist(false, n0) + false ' + bits0, false ' + bits1)) = sgn(bitsand(bits1, false ' + bits0)), n0 = 0, bits1 = []

Rule argument

Additional information

Used simplifier rules: ⊦ (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 ≠ [];