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Proof step 1 from proof nodups-interval-size (conclusion)

¬ dups(ints), ∀ i. i ∈ ints → j0 < i ∧ i ≤ j1, ints ≠ [] ⊦ n→i(# ints) ≤ j1 - j0

User applied rule induction

And obtained the following new goals

Proof step 2:
¬ dups(ints) ∧ (∀ i. i ∈ ints → j0 < i ∧ i ≤ j1) ∧ ints ≠ [], ∀ ints0, j0, j1. # ints0 < # ints → ¬ dups(ints0) ∧ (∀ i. i ∈ ints0 → j0 < i ∧ i ≤ j1) ∧ ints0 ≠ [] → n→i(# ints0) ≤ j1 - j0 ⊦ n→i(# ints) ≤ j1 - j0

Rule argument

indvar: # ints wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # ints