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Proof step 12 from proof bitsand-cast-01 (previous step)

∃ bits0, bits1. bits = bits0 + bits1 ∧ # bits1 = n, n ≤ # bits ⊦ bits = [], bits0 = [], lastn(n, fillsgn(n, bitsand(lastn(n, bits), bits0))) = lastn(n, fillsgn(n, bitsand(bits, bits0)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
⊦ bits2 + bits1 = [], bits0 = [], lastn(# bits1, fillsgn(# bits1, bitsand(lastn(# bits1, bits2 + bits1), bits0))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits0)))

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m ≤ m + n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;