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Proof step 10 from proof bitsand-cast-05 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 12:
# bits ≤ # bits1 ∧ bits ≠ [], # bits < # bits1 ⊦ bits1 = [], sgn(bitsand(lastn(# bits1, mklist(bits.first, # bits1 - # 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, # bits1] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m; Used terms: bits, # bits1