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Proof step 3 from proof rev-at-h (previous step)

m < n, m < # ar, n ≤ # ar ⊦ rev(ar, n)[m] = ar[# ar - m + 1]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
# ar = n0 + m + 1, m < # ar, m < n, n ≤ # ar, m + 1 ≤ # ar ⊦ rev(ar, n)[m] = ar[n0]

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# ar, m + 1, n0]

Additional information

Used simplifier rules: ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # ar, m + 1, n0