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Proof step 63 from proof shiftzero-pos (previous step)

# int2bits(i) = i→n(j), 0 ≤ i, i→n(j) < n ⊦ bits2int(firstn(n, mklist(false, i→n(j)) + mklist(false, n - i→n(j)) + int2bits(i))) = 0, j = 0, mklist(false, i→n(j)) + mklist(false, n - i→n(j)) = mklist(false, n)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 64:
n = n0 + i→n(j) ∧ i→n(j) ≤ n, # int2bits(i) = i→n(j), 0 ≤ i, i→n(j) < n ⊦ bits2int(firstn(n, mklist(false, i→n(j)) + mklist(false, n0) + int2bits(i))) = 0, j = 0, mklist(false, i→n(j)) + mklist(false, n0) = mklist(false, n)

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, i→n(j), 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, i→n(j), n0