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Proof step 9 from proof is_array-init-01 (previous step)

⊦ r = r0, (∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → r -- j0 ' ∈ st) ↔ is_arrayref(r, i, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 8:
⊦ r = r0, (∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → r -- j0 ' ∈ st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)

Rule argument

[speclemmaarg: ,is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st) ,[st, i, r] → [st, i, r] ,F ,storearrays , ,is_arrayref ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, i, r)]]