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Proof step 32 from proof fill-sgn-01 (previous step)

n1 + # bits0 = n + # sgn(boolvar ' + bits0), # sgn(boolvar ' + bits0) ≤ n1 + # bits0, # sgn(boolvar ' + bits0) ≤ 1 + # bits0, ∀ n0. ¬ n0 < # bits0 → fillsgn(n0, sgn(bits0)) = fillsgn(n0, bits0) ⊦ n1 = 0, mklist(boolvar, n) + sgn(boolvar ' + bits0) = mklist(boolvar, n1) + bits0, (¬ boolvar) ∈ bits0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
¬ (¬ boolvar) ∈ bits ⊦ sgn(boolvar ' + bits) = boolvar '
Proof step 34:
¬ (¬ boolvar) ∈ bits0, n1 + # bits0 = n + # boolvar ', # boolvar ' ≤ n1 + # bits0, # boolvar ' ≤ 1 + # bits0, ∀ n0. ¬ n0 < # bits0 → fillsgn(n0, sgn(bits0)) = fillsgn(n0, bits0) ⊦ n1 = 0, mklist(boolvar, n) + boolvar ' = mklist(boolvar, n1) + bits0, (¬ boolvar) ∈ bits0

Rule argument

name: sgn-in rotate: F subst: [bits, boolvar] → [bits0, boolvar]

Additional information

Used terms: bits0, boolvar