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Proof step 7 from proof isarrayref-mod (previous step)

onlyModified(r0, st, st0), j < i, 0 ≤ j, 0 < i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r -- j ' ∈ st ⊦ r = r0, r -- j ' ∈ st0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ onlyModified(r, st1, st2) ↔ (∀ rk. rk ∈ st1 ↔ rk ∈ st2) ∧ (∀ r0, sk. r0 ≠ r → st1[r0 -- sk] = st2[r0 -- sk]) ∧ (r -- _type ∈ st1 → st1[r -- _type] = st2[r -- _type]) ∧ (r -- _length ∈ st1 → st1[r -- _length] = st2[r -- _length])
Proof step 6:
(∀ rk. rk ∈ st ↔ rk ∈ st0) ∧ (∀ r1, sk. r1 ≠ r0 → st[r1 -- sk] = st0[r1 -- sk]) ∧ (r0 -- _type ∈ st → st[r0 -- _type] = st0[r0 -- _type]) ∧ (r0 -- _length ∈ st → st[r0 -- _length] = st0[r0 -- _length]), j < i, 0 ≤ j, 0 < i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r -- j ' ∈ st ⊦ r = r0, r -- j ' ∈ st0

Rule argument

[speclemmaarg: , onlyModified(r, st1, st2) ↔ (∀ rk. rk ∈ st1 ↔ rk ∈ st2) ∧ (∀ r0, sk. r0 ≠ r → st1[r0 -- sk] = st2[r0 -- sk]) ∧ (r -- _type ∈ st1 → st1[r -- _type] = st2[r -- _type]) ∧ (r -- _length ∈ st1 → st1[r -- _length] = st2[r -- _length]) ,[st2, st1, r] → [st0, st, r0] ,F ,storefunsx , ,onlyModified ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, st, r0)]]