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Proof step 5 from proof valid-idx-imp-1 (previous step)

n < # kar, ∀ m. ¬ n < m → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ n ≤ # kar ∧ (∀ m. m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
m < # kar, m < n, n < # kar, m + 1 < # kar, ∀ m. ¬ n < m → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (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%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → m ≤ n; (s)