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Proof step 8 from proof in-1dim-07 (previous step)

∀ st, val, fs, r0, i0. i→n(i0) < i→n(i) → (true → (r0 -- fs ' ∈ addarray(r0, val, i0, st) ↔ r0 -- fs ' ∈ st)) ⊦ r0 -- fs ' ∈ addarray(r0, val, i, st) ↔ r0 -- fs ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ i > 0 → addarray(r, val, i, st) = (addarray(r, val, i - 1, st)[r -- (i - 1) ', val])
Proof step 3:
⊦ i ≤ 0 → addarray(r, val, i, st) = st
Proof step 7:
i > 0, ∀ st, val, fs, r0, i0. i→n(i0) < i→n(i) → (true → (r0 -- fs ' ∈ addarray(r0, val, i0, st) ↔ r0 -- fs ' ∈ st)) ⊦ r0 -- fs ' ∈ (addarray(r0, val, i - 1, st)[r0 -- (i - 1) ', val]) ↔ r0 -- fs ' ∈ st

Rule argument

[crewrite-arg: addarray-rec, F, [st, i, val, r] → [st, i, val, r0]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i > j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i])], [EXTRATERMS : (st, i, val, r0)]]