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Proof step 8 from proof rev-at-h (previous step)

# ar = n2 + n1 + 1, # ar = n0 + m + 1, n0 + m = n1 + n2, m ≤ n1 + n2, m ≤ n2 + n1, m < # ar, m ≤ n1, n1 < # ar, ∀ ar, n0, m. # ar = n0 + m + 1 ∧ m < n1 ∧ n1 ≤ # ar ∧ m < # ar → # ar = 0 ∨ rev(ar, n1)[m] = ar[n0] ∨ n1 = 0 ⊦ # ar = 0, rev(ar, n1)[n1, ar[n2]][m] = ar[n0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ m ≠ n → ar[n, a][m] = ar[m]
Proof step 10:
¬ m ≠ n1, # ar = n2 + n1 + 1, # ar = n0 + m + 1, n0 + m = n1 + n2, m ≤ n1 + n2, m ≤ n2 + n1, m < # ar, m ≤ n1, n1 < # ar, ∀ ar, n0, m. # ar = n0 + m + 1 ∧ m < n1 ∧ n1 ≤ # ar ∧ m < # ar → # ar = 0 ∨ rev(ar, n1)[m] = ar[n0] ∨ n1 = 0 ⊦ # ar = 0, rev(ar, n1)[n1, ar[n2]][m] = ar[n0]
Proof step 16:
m ≠ n1, # ar = n2 + n1 + 1, # ar = n0 + m + 1, n0 + m = n1 + n2, m ≤ n1 + n2, m ≤ n2 + n1, m < # ar, m ≤ n1, n1 < # ar, ∀ ar, n0, m. # ar = n0 + m + 1 ∧ m < n1 ∧ n1 ≤ # ar ∧ m < # ar → # ar = 0 ∨ rev(ar, n1)[m] = ar[n0] ∨ n1 = 0 ⊦ # ar = 0, rev(ar, n1)[m] = ar[n0]

Rule argument

spec: array inst: 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: rewrite

Additional information

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