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Proof step 13 from proof valid-idx-remlast (previous step)

kar[m4] = key-index(key1, m3), ar[n, ar[n].idx:= 0][m1] = elemindex(a, m2), kar[m] = key-index(key, n), kar[0, key-index(key, n)][m4] = key-index(key0, m1), ar[m3] = elemindex(a0, m4), m4 + 1 < # kar, m3 < # ar, m < # kar, m4 < m, m4 < # kar, ∀ m0. ¬ m < m0 → kar[m0].idx < # ar ∧ ar[kar[m0].idx].idx = m0 ⊦ m1 < # ar ∧ m2 = m4

User applied rule all left

And obtained the following new goals

Proof step 14:
ar[m3] = elemindex(a0, m4), kar[0, key-index(key, n)][m4] = key-index(key0, m1), kar[m] = key-index(key, n), ar[n, ar[n].idx:= 0][m1] = elemindex(a, m2), kar[m4] = key-index(key1, m3), m4 < # kar, m4 < m, m < # kar, m3 < # ar, m4 + 1 < # kar, ¬ m < m → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m, ∀ m0. ¬ m < m0 → kar[m0].idx < # ar ∧ ar[kar[m0].idx].idx = m0 ⊦ m1 < # ar ∧ m2 = m4

Rule argument

pos: left 11 terms: m abort: F discard: F computed: T

Additional information

Used terms: m