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Proof step 8 from proof in-1dim-other-index-01 (previous step)

0 ≤ i0, r -- i ' ∈ (addarray(r, val, i0, st)[r -- i0 ', val]), i < 0 ∨ i0 < i, ∀ st, val, r, i, j0. i→n(j0) < i→n(i0 + 1) → (true → (i < 0 ∨ j0 ≤ i → (r -- i ' ∈ addarray(r, val, j0, st) ↔ r -- i ' ∈ st))) ⊦ r -- i ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ rk ≠ rk0 → (rk ∈ st[rk0, val] ↔ rk ∈ st)
Proof step 7:
r -- i ' ≠ r -- i0 ', 0 ≤ i0, r -- i ' ∈ addarray(r, val, i0, st), i < 0 ∨ i0 < i, ∀ st, val, r, i, j0. i→n(j0) < i→n(i0 + 1) → (true → (i < 0 ∨ j0 ≤ i → (r -- i ' ∈ addarray(r, val, j0, st) ↔ r -- i ' ∈ st))) ⊦ r -- i ' ∈ st

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (rk ∈ st[rk0, val] ↔ rk ∈ st) ,[val, rk0, st, rk] → [val, r -- i0 ', addarray(r, val, i0, st), r -- i '] ,F ,store ,javastore ,in-neq ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPFORWARD : ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPFORWARD : ⊦ j < i ∧ i ≤ 0 → j < 0], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ ¬ i < i])], [EXTRATERMS : (val, r -- i0 ', addarray(r, val, i0, st), r -- i ')]]