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Proof step 139 from proof putarray-addarray-01 (previous step)

0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, i0 < 0 ∨ i + n→i(# vals) ≤ i0, r -- i0 ' ∈ addarray(r, ty, j, st) ∨ i ≤ i0 ∧ i0 < i + n→i(# vals) ⊦ r -- i0 ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 137:
⊦ i < 0 ∨ j ≤ i → (r -- i ' ∈ addarray(r, ty, j, st) ↔ r -- i ' ∈ st)
Proof step 138:
⊦ 0 ≤ j ∧ j < i → r -- j ' ∈ addarray(r, ty, i, st)

Rule argument

[crewrite-arg: in-1dim-other-index , F , [st, j, ty, i, r] → [st, j, ty, i0, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPFORWARD : ⊦ j < i ∧ i ≤ 0 → j < 0], [CSIMPSEQ : ⊦ i < 0 ∧ 0 ≤ j → i < j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1])], [EXTRATERMS : (st, j, ty, i0, r)]]