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Proof step 21 from proof valid-idx-move-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
ar[m1] = elemindex(a0, m3), kar[m3] = key-index(key, m1), kar[m2] = key-index(key0, m1), m2 < # kar, m1 < # ar, m3 < # kar, m2 < m3, m2 + 1 < # kar, ∀ m. ¬ m3 < m → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ m4 = m2

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)% ⊦ elemindex(a, m) = elemindex(a0, m0) ↔ a = a0 ∧ m = m0; (ws)% ⊦ elemindex(a, m).idx:= m0 = elemindex(a, m0); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic