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Proof step 2 from proof fill-fill (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
n = n0 + # bits, # bits ≤ n ⊦ bits = [], fillsgn(n, bits) = mklist(bits.first, n0) + 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: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, # bits, n0