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Proof step 42 from proof bitsand-cast-05 (previous step)

#(boolvar ' + bits) = #(false ' + bits1) ∧ 1 < #(boolvar ' + bits), # bits = # bits1 ⊦ sgn(bitsand(bits, false ' + bits1)) = sgn(((boolvar ' + bits).first ∧ (false ' + bits1).first)' + bitsand((boolvar ' + bits).rest, (false ' + bits1).rest)), bits1 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# bits = # bits1 ⊦ bits1 = [], sgn(bitsand(bits, false ' + bits1)) = sgn(false ' + bitsand(bits, bits1)), bits = []

Rule argument

Additional information

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