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Proof step 8 from proof inv-fill (previous step)

# bits < n ⊦ bits = [], mklist(¬ bits.first, n - # bits) + bitsinvert(bits) = fillsgn(n, bitsinvert(bits))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
n = n0 + # bits ∧ # bits ≤ n, # bits < n ⊦ bits = [], mklist(¬ bits.first, n0) + bitsinvert(bits) = fillsgn(n, bitsinvert(bits))

Rule argument

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