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Proof step 24 from proof valid-idx-xhg (previous step)

ar0[n0].idx:= m0.idx:= m0 = elemindex(a, m3), kar[m0] = key-index(key1, n0), ar[n0] = elemindex(a1, m0), m0 < # kar, m0 < n, n0 < # ar, n ≤ # kar, ∀ m. m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ m3 = m0

User applied rule structural induction

And closed the goal!

Rule argument

term: ar0[n0]

Additional information

Used simplifier rules: elem-index freely generated by elemindex;;% ⊦ elemindex(a, m).idx:= m0 = elemindex(a, m0); (s)% ⊦ elemindex(a, m) = elemindex(a0, m0) ↔ a = a0 ∧ m = m0; (ws)