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Proof step 12 from proof in-1dim-other-index-01 (previous step)

r -- i ' ∈ addarray(r, val, j, st), r ∈ addarray(r, val, j, st), 0 < j, i < 0 ∨ j ≤ i, ∀ st, val, r, i, j0. i→n(j0) < i→n(j) → (true → (i < 0 ∨ j0 ≤ i → (r -- i ' ∈ addarray(r, val, j0, st) ↔ r -- i ' ∈ st))) ⊦ r -- i ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i > 0 → addarray(r, val, i, st) = (addarray(r, val, i - 1, st)[r -- (i - 1) ', val])
Proof step 11:
j > 0, r -- i ' ∈ (addarray(r, val, j - 1, st)[r -- (j - 1) ', val]), r ∈ (addarray(r, val, j - 1, st)[r -- (j - 1) ', val]), 0 < j, i < 0 ∨ j ≤ i, ∀ st, val, r, i, j0. i→n(j0) < i→n(j) → (true → (i < 0 ∨ j0 ≤ i → (r -- i ' ∈ addarray(r, val, j0, st) ↔ r -- i ' ∈ st))) ⊦ r -- i ' ∈ st

Rule argument

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

Additional information

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