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Proof step 27 from proof fill-sgn-01 (previous step)

# bits + n1 = 1 + n, mklist(boolvar, # bits) = bits, ∀ n0. ¬ n0 ≤ # bits + # bits1 → fillsgn(n0, sgn(bits + (¬ boolvar)' + bits1)) = fillsgn(n0, bits + (¬ boolvar)' + bits1) ⊦ mklist(boolvar, n + 1) = mklist(boolvar, n1) + mklist(boolvar, # bits), n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n)
Proof step 29:
# bits + n1 = 1 + n, mklist(boolvar, # bits) = bits, ∀ n0. ¬ n0 ≤ # bits + # bits1 → fillsgn(n0, sgn(bits + (¬ boolvar)' + bits1)) = fillsgn(n0, bits + (¬ boolvar)' + bits1) ⊦ mklist(boolvar, n + 1) = mklist(boolvar, n1 + # bits), n1 = 0

Rule argument

seq: ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n) subst: [n, m, boolvar] → [# bits, n1, boolvar] rotate: T spec: list-last inst: bitlista name: mk-plus

Additional information

Used terms: # bits, n1, boolvar