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Proof step 10 from proof init-switch (previous step)

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

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