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Proof step 9 from proof in-1dim-other-index-01 (previous step)

j = i0 + 1, 0 < j, r -- i ' ∈ (addarray(r, val, i0, st)[r -- i0 ', val]), 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
0 ≤ i0, r -- i ' ∈ (addarray(r, val, i0, st)[r -- i0 ', val]), i < 0 ∨ i0 < i, ∀ st, val, r, i, j0. i→n(j0) < i→n(i0 + 1) → (true → (i < 0 ∨ j0 ≤ i → (r -- i ' ∈ addarray(r, val, j0, st) ↔ r -- i ' ∈ st))) ⊦ r -- i ' ∈ st

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ st[r -- sk, val]], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0])]]