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Proof step 6 from proof fill-rec (previous step)

# bits0 < m ⊦ fillsgn(m + 1, boolvar ' + bits0) = boolvar ' + mklist(boolvar, m - # bits0) + bits0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
m = n + # bits0 ∧ # bits0 ≤ m, # bits0 < m ⊦ fillsgn(m + 1, boolvar ' + bits0) = boolvar ' + mklist(boolvar, n) + bits0

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [m, # bits0, n] 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: m, # bits0, n