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Proof step 7 from proof bitsand-cast-04 (previous step)

# bits1 < n, # bits < n ⊦ sgn(bitsand(lastn(n, fillsgn(n, bits)), false ' + bits1)) = sgn(bitsand(bits, false ' + bits1)), bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 9:
# bits ≤ n ∧ bits ≠ [], # bits1 < n, # bits < n ⊦ sgn(bitsand(lastn(n, mklist(bits.first, n - # bits) + bits), false ' + bits1)) = sgn(bitsand(bits, false ' + bits1)), bits = []

Rule argument

seq: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [bits, n] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m; Used terms: bits, n