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Proof step 8 from proof putar-in-02 (previous step)

∀ r0, j0, i0, st0. r0 -- j0 ' ∈ putArray(vals0, r0, i0, st0) ↔ r0 -- j0 ' ∈ st0 ∨ i0 ≤ j0 ∧ j0 < i0 + n→i(# vals0) ⊦ r -- j ' ∈ (putArray(vals0, r, i + 1, st)[r -- i ', val]) ↔ r -- j ' ∈ st ∨ ¬ n→i(# vals0) + i < j ∧ ¬ j < i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
sk ≠ sk0 ⊦ r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st
Proof step 7:
j ' ≠ i ', ∀ r0, j0, i0, st0. r0 -- j0 ' ∈ putArray(vals0, r0, i0, st0) ↔ r0 -- j0 ' ∈ st0 ∨ i0 ≤ j0 ∧ j0 < i0 + n→i(# vals0) ⊦ r -- j ' ∈ putArray(vals0, r, i + 1, st) ↔ r -- j ' ∈ st ∨ ¬ n→i(# vals0) + i < j ∧ ¬ j < i

Rule argument

[speclemmaarg: sk ≠ sk0 ,r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st ,[val, sk0, st, sk, r] → [val, i ', putArray(vals0, r, i + 1, st), j ', r] ,F ,javastore , ,instore-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPSEQ : ⊦ r ∈ st[r -- sk, val]], [CSIMPSEQ : ⊦ ¬ i < i], [CSIMPSEQ : ⊦ i ≤ i], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (val, i ', putArray(vals0, r, i + 1, st), j ', r)]]