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Proof step 32 from proof fill-lastn-03 (previous step)

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

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, # bits, n0] rotate: T spec: nat inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ m + n < m + n0 ↔ n < n0;% ⊦ m ≤ n → (n < m ↔ false);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, # bits, n0