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Proof step 7 from proof putArray-put-switch-02 (previous step)

is_fskey(sk) ∨ r0 ≠ r, ∀ sk0, r1, r2, i0, st0, val1. ¬ is_indexkey(sk0) ∨ r1 ≠ r2 → putArray(vals0, r2, i0, st0[r1 -- sk0, val1]) = (putArray(vals0, r2, i0, st0)[r1 -- sk0, val1]) ⊦ (putArray(vals0, r, i + 1, st[r0 -- sk, val])[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- i ', val0][r0 -- sk, 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 6:
r0 -- sk ≠ r -- i ', is_fskey(sk) ∨ r0 ≠ r, ∀ sk0, r1, r2, i0, st0, val1. ¬ is_indexkey(sk0) ∨ r1 ≠ r2 → putArray(vals0, r2, i0, st0[r1 -- sk0, val1]) = (putArray(vals0, r2, i0, st0)[r1 -- sk0, val1]) ⊦ (putArray(vals0, r, i + 1, st[r0 -- sk, val])[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r0 -- sk, val][r -- i ', val0])

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [val, r0 -- sk, val0, r -- i ', putArray(vals0, r, i + 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 ')])], [EXTRATERMS : (val, r0 -- sk, val0, r -- i ', putArray(vals0, r, i + 1, st))]]