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Proof step 4 from proof fill-sgn-01 (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
n = n1 + # bits0 ∧ # bits0 ≤ n, # bits0 < n, ∀ n0. ¬ n0 < # bits0 → fillsgn(n0, sgn(bits0)) = fillsgn(n0, bits0) ⊦ fillsgn(n, sgn(boolvar ' + bits0)) = mklist(boolvar, n1) + bits0

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, # bits0, n1] rotate: T spec: nat inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m;%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, # bits0, n1