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Proof step 7 from proof copy-arref (previous step)

⊦ r1 = r0, (∀ j0. ¬ j0 < 0 ∧ ¬ i1 ≤ j0 → r1 -- j0 ' ∈ st) ↔ (∀ j. 0 ≤ j ∧ j < i1 → r1 -- j ' ∈ st)

User applied rule case distinction

And obtained the following new goals

Proof step 4:
∀ j0. ¬ j0 < 0 ∧ ¬ i1 ≤ j0 → r1 -- j0 ' ∈ st ⊦ ∀ j. 0 ≤ j ∧ j < i1 → r1 -- j ' ∈ st, r1 = r0
Proof step 6:
∀ j. 0 ≤ j ∧ j < i1 → r1 -- j ' ∈ st ⊦ ∀ j0. ¬ j0 < 0 ∧ ¬ i1 ≤ j0 → r1 -- j0 ' ∈ st, r1 = r0

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]