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Proof step 13 from proof valid-idx-move-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic% ⊦ key-index(key, m) = key-index(key0, m0) ↔ key = key0 ∧ m = m0; (ws)% ⊦ m < # kar → kar[m, ki][m] = ki; (s)