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Proof step 10 from proof putar-rew (previous step)

n→i(# vals0) + j < sk .index ∨ r0 ≠ r ∨ is_fskey(sk) ∨ sk .index < j, ∀ r1, r2, sk0, j0, st0, val1. ¬ is_indexkey(sk0) ∨ r1 ≠ r2 ∨ ¬ j0 ≤ sk0 .index ∨ ¬ sk0 .index < n→i(# vals0) + j0 → (putArray(vals0, r2, j0, st0)[r1 -- sk0, val1]) = putArray(vals0, r2, j0, st0[r1 -- sk0, val1]) ⊦ (putArray(vals0, r, j + 1, st)[r -- j ', val][r0 -- sk, val0]) = (putArray(vals0, r, j + 1, st[r0 -- sk, val0])[r -- j ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 9:
r0 -- sk ≠ r -- j ', n→i(# vals0) + j < sk .index ∨ r0 ≠ r ∨ is_fskey(sk) ∨ sk .index < j, ∀ r1, r2, sk0, j0, st0, val1. ¬ is_indexkey(sk0) ∨ r1 ≠ r2 ∨ ¬ j0 ≤ sk0 .index ∨ ¬ sk0 .index < n→i(# vals0) + j0 → (putArray(vals0, r2, j0, st0)[r1 -- sk0, val1]) = putArray(vals0, r2, j0, st0[r1 -- sk0, val1]) ⊦ (putArray(vals0, r, j + 1, st)[r0 -- sk, val0][r -- j ', val]) = (putArray(vals0, r, j + 1, st[r0 -- sk, val0])[r -- j ', val])

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [val0, r0 -- sk, val, r -- j ', putArray(vals0, r, j + 1, st)] ,F ,store ,javastore ,rew ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ (st[rk, val][rk, val0]) = st[rk, val0]], [CSIMPSEQ : ⊦ ¬ is_fskey(i ')], [CSIMPSEQ : ⊦ i ' .index = 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 : (val0, r0 -- sk, val, r -- j ', putArray(vals0, r, j + 1, st))]]