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Proof step 6 from proof in-1dim-other-index (previous step)

r -- i ' ∈ addarray(r, initial_value(ty), j, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(j)]), r ∈ addarray(r, initial_value(ty), j, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(j)]), i < 0 ∨ j ≤ i ⊦ r -- i ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ i < 0 ∨ j ≤ i → (r -- i ' ∈ addarray(r, val, j, st) ↔ r -- i ' ∈ st)
Proof step 5:
⊦ 0 ≤ j ∧ j < i → r -- j ' ∈ addarray(r, val, i, st)

Rule argument

[crewrite-arg: in-1dim-other-index-01 , F , [st, j, val, i, r] → [st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(j)], j, initial_value(ty), i, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ _type ≠ i '], [CSIMPSEQ : sk ≠ sk0 ⊦ r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st], [CSIMPSEQ : ⊦ _length ≠ i '], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (st[r -- _type, typeval(mkarraytype(ty))] [r -- _length, intval(j) ], j, initial_value(ty), i, r)]]