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Proof step 30 from proof bitsand-cast-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
# 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)))

Rule argument

Additional information

Used simplifier rules: bitsand-app: ⊦ # bits = # bits1 ∧ bits0 ≠ [] ∧ bits2 ≠ [] ∧ bits ≠ [] → bitsand(bits0 + bits, bits2 + bits1) = bitsand(bits0, bits2) + bitsand(bits, bits1);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;