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Proof step 12 from proof fill-sgn-01 (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
n1 + # bits0 = n + # sgn(boolvar ' + bits0), # sgn(boolvar ' + bits0) ≤ n1 + # bits0, ∀ n0. ¬ n0 < # bits0 → fillsgn(n0, sgn(bits0)) = fillsgn(n0, bits0) ⊦ n1 = 0, mklist(boolvar, n) + sgn(boolvar ' + bits0) = mklist(boolvar, n1) + bits0

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n1 + # bits0, # sgn(boolvar ' + bits0), n] rotate: T spec: nat inst: name: elim-sub

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n1 + # bits0, # sgn(boolvar ' + bits0), n