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Proof step 5 from proof putArray-in (previous step)

r -- i0 ' ∈ putArray(vals0, r, i + 1, st[r -- i ', val]), r ∈ putArray(vals0, r, i + 1, st[r -- i ', val]), ∀ rk, r, i, st. rk ∈ putArray(vals0, r, i, st) ↔ rk ∈ st ∨ rk .ref = r ∧ is_indexkey(rk .key) ∧ i ≤ rk .key .index ∧ rk .key .index < i + n→i(# vals0), i0 = i ∨ i < i0 ∧ i0 ≤ i + n→i(# vals0) ⊦ r -- i0 ' ∈ st, ¬ n→i(# vals0) + i < i0 ∧ ¬ i0 < i

User applied rule case distinction

And closed the goal!

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])]]