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Proof step 76 from proof shiftzero-pos (previous step)

i→n(j) < # int2bits(i), 0 ≤ i, # int2bits(i) < n, i→n(j) < n, i→n(j) + 1 < n, (n - i→n(j)) + # int2bits(i) < n ⊦ # int2bits(i) = i→n(j), bits2int(mklist(false, i→n(j)) + firstn(n - i→n(j), mklist(false, n - # int2bits(i)) + int2bits(i))) = bits2int(firstn(# int2bits(i) - i→n(j), int2bits(i))), firstn(# int2bits(i) - i→n(j), int2bits(i)).first

User applied rule insert elim lemma

And closed the goal!

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 → m ≤ n;% ⊦ m < m + n ↔ n ≠ 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ m < n → ¬ n < m;%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, i→n(j), n0