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Proof step 8 from proof valid-idx-xhg (previous step)

kar[m0, key-index(key0, n0)][m1, key-index(key1, n1)][m] = key-index(key, m2), kar[m1] = key-index(key0, n0), kar[m0] = key-index(key1, n1), ar[n0, ar[n0].idx:= m0][n1, ar[n0, ar0[n0].idx:= m0][n1].idx:= m1][m2] = elemindex(a, m3), m1 < n, m0 < n, m1 < # kar, m0 < # kar, m < n, m < # kar, n ≤ # kar, ∀ m. m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ m2 < # ar ∧ m3 = m

User applied rule all left

And obtained the following new goals

Proof step 9:
ar[n0, ar[n0].idx:= m0][n1, ar[n0, ar0[n0].idx:= m0][n1].idx:= m1][m2] = elemindex(a, m3), kar[m0] = key-index(key1, n1), kar[m1] = key-index(key0, n0), kar[m0, key-index(key0, n0)][m1, key-index(key1, n1)][m] = key-index(key, m2), m < # kar, m < n, m0 < # kar, m1 < # kar, m0 < n, m1 < n, n ≤ # kar, m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m, ∀ m. m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ m2 < # ar ∧ m3 = m

Rule argument

pos: left 12 terms: m abort: F discard: F computed: T

Additional information

Used terms: m