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Proof step 5 from proof bitsand-cast-01 (previous step)

# bits < n ⊦ lastn(n, fillsgn(n, bitsand(lastn(n, fillsgn(n, bits)), bits0))) = lastn(n, fillsgn(n, bitsand(bits, bits0))), bits0 = [], bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ n = # bits → lastn(n, bits) = bits
Proof step 7:
n ≠ # fillsgn(n, bits), # bits < n ⊦ lastn(n, fillsgn(n, bitsand(lastn(n, fillsgn(n, bits)), bits0))) = lastn(n, fillsgn(n, bitsand(bits, bits0))), bits0 = [], bits = []

Rule argument

seq: ⊦ n = # bits → lastn(n, bits) = bits subst: [bits, n] → [fillsgn(n, bits), n] rotate: F spec: list-del inst: bitlista name: lastN-all

Additional information

Used simplifier rules: bitsand-fillsgn: ⊦ bits ≠ [] ∧ bits0 ≠ [] → fillsgn(n, bitsand(fillsgn(n, bits), bits0)) = fillsgn(n, bitsand(bits, bits0)); Used terms: fillsgn(n, bits), n