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Proof step 15 from proof valid-idx-move-last (previous step)

ar[m1].idx:= m0 = elemindex(a, m4), kar[m] = key-index(key, m1), m0 + 1 < # kar, m < # kar, m0 < m, m1 < # ar, m0 < # kar, ¬ m < m → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ m4 = m0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
ar[m1].idx:= m0 = elemindex(a, m4), kar[ar[m1].idx] = key-index(key, m1), m0 + 1 < # kar, m0 < ar[m1].idx, ar[m1].idx < # kar, m0 < # kar, m1 < # ar ⊦ m4 = m0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ key-index(key, m).idx = m; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ ¬ n < n; (s)