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Proof step 10 from proof switch-addarray-addclass-01 (previous step)

∀ st, fis, class, val, r, i0. i→n(i0) < i→n(i) → (true → r = jvmref ∨ addarray(r, val, i0, addclass(class, fis, st)) = addclass(class, fis, addarray(r, val, i0, st))) ⊦ addarray(r, val, i, addclass(class, fis, st)) = addclass(class, fis, addarray(r, val, i, st)), r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ i > 0 → addarray(r, val, i, st) = (addarray(r, val, i - 1, st)[r -- (i - 1) ', val])
Proof step 2:
⊦ i ≤ 0 → addarray(r, val, i, st) = st
Proof step 9:
i > 0, ∀ st, fis, class, val, r, i0. i→n(i0) < i→n(i) → (true → r = jvmref ∨ addarray(r, val, i0, addclass(class, fis, st)) = addclass(class, fis, addarray(r, val, i0, st))) ⊦ (addarray(r, val, i - 1, addclass(class, fis, st))[r -- (i - 1) ', val]) = addclass(class, fis, addarray(r, val, i, st)), r = jvmref

Rule argument

[crewrite-arg: addarray-rec , F , [st, i, val, r] → [addclass(class, fis, st), i, val, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i > j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i])], [EXTRATERMS : (addclass(class, fis, st), i, val, r)]]