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Proof step 33 from proof bitsand-cast-01 (previous step)

¬ # bits1 ≤ #(bitsand(bits2, bits3) + bitsand(bits1, bits)), # bits = # bits1 ⊦ bits2 + bits1 = [], bits2 = [], bits3 + bits = [], bits1 = [], bits3 = [], lastn(# bits1, fillsgn(# bits1, bitsand(bits3 + bits, bits1))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2, bits3) + bitsand(bits1, bits)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
# bits = # bits1, # bitsand(bits2, bits3) + # bitsand(bits1, bits) < # bits1 ⊦ lastn(# bits1, fillsgn(# bits1, bitsand(bits3 + bits, bits1))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2, bits3) + bitsand(bits1, bits))), bits3 = [], bits1 = [], bits3 + bits = [], bits2 = [], bits2 + bits1 = []

Rule argument

Additional information

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