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Proof step 11 from proof rev-at-h (previous step)

# ar = n2 + n1 + 1, # ar = n0 + m + 1, n0 + m = n1 + n2, m < # ar, n1 < # ar, m ≤ n1 + n2, m ≤ n2 + n1, m ≤ n1, ∀ ar, n0, m. # ar = n0 + m + 1 ∧ m < # ar ∧ m < n1 ∧ n1 ≤ # ar → rev(ar, n1)[m] = ar[n0] ⊦ rev(ar, n1)[n1, ar[n2]][m] = ar[n0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ m ≠ n → ar[n, a][m] = ar[m]
Proof step 13:
# ar = n0 + m + 1, # ar = n2 + n1 + 1, n0 + m = n1 + n2, m = n1, n1 < # ar, m < # ar, m ≤ n1, m ≤ n2 + n1, m ≤ n1 + n2, ∀ ar, n0, m. # ar = n0 + m + 1 ∧ m < # ar ∧ m < n1 ∧ n1 ≤ # ar → rev(ar, n1)[m] = ar[n0] ⊦ rev(ar, n1)[n1, ar[n2]][m] = ar[n0]
Proof step 19:
# ar = n0 + m + 1, # ar = n2 + n1 + 1, n0 + m = n1 + n2, n1 < # ar, m < # ar, m ≤ n1, m ≤ n2 + n1, m ≤ n1 + n2, ∀ ar, n0, m. # ar = n0 + m + 1 ∧ m < # ar ∧ m < n1 ∧ n1 ≤ # ar → rev(ar, n1)[m] = ar[n0] ⊦ rev(ar, n1)[m] = ar[n0], m = n1

Rule argument

spec: array name: Put-other seq: ⊦ m ≠ n → ar[n, a][m] = ar[m] subst: [m, a, n, ar] → [m, ar[n2], n1, rev(ar, n1)] flags: <all paths>

Additional information

Used terms: m, ar[n2], n1, rev(ar, n1)