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Proof step 16 from proof valid-idx-remlast (previous step)

ar[n, ar[n].idx:= 0][m1] = elemindex(a, m2), kar[m4] = key-index(key1, m3), ar[m3] = elemindex(a0, m4), kar[0, key-index(key, n)][m4] = key-index(key0, m1), kar[m0] = key-index(key, n), ar[n] = elemindex(a1, m0), m3 < # ar, m4 + 1 < # kar, m4 < m0, m4 < # kar, m0 < # kar, n < # ar, ∀ m. ¬ m0 < m → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ m1 < # ar ∧ m2 = m4

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
kar[m4] = key-index(key1, m3), ar[m3] = elemindex(a0, m4), kar[0, key-index(key, n)][m4] = key-index(key0, m1), kar[m0] = key-index(key, n), ar[n] = elemindex(a1, m0), ar[n, elemindex(a1, 0)][m1] = elemindex(a, m2), m3 < # ar, m4 + 1 < # kar, m4 < m0, m4 < # kar, m0 < # kar, n < # ar, ∀ m. ¬ m0 < m → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ m1 < # ar ∧ m2 = m4

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)% ⊦ elemindex(a, m).idx:= m0 = elemindex(a, m0); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic