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Proof step 48 from proof bitsand-cast-01 (previous step)

¬(¬ bits1.first ∧ # bits1 ≤ #(bits3 + bits) ∧ bits1 ≠ []), # bits1 = # bitsand(bits1, bits), # bits = # bits1, # bitsand(bits3 + bits, bits1) < # bits1 ⊦ bits2 + bits1 = [], bits2 = [], bits3 + bits = [], bits1 = [], bits3 = [], lastn(# bits1, fillsgn(# bits1, bitsand(bits3 + bits, bits1))) = bitsand(bits1, bits)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
# bits = # bits1, # bits1 = # bitsand(bits1, bits), # bitsand(bits3 + bits, bits1) < # bits3 + # bits1, bits1.first, # bitsand(bits3 + bits, bits1) < # bits1 ⊦ lastn(# bits1, fillsgn(# bits1, bitsand(bits3 + bits, bits1))) = bitsand(bits1, bits), bits3 = [], bits1 = [], bits3 + bits = [], bits2 = [], bits2 + bits1 = []

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ ¬ m + n < m;% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;