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Proof step 4 from proof putar-in-02 (previous step)

r -- j ' ∈ putArray(vals0, r, i + 1, st) ↔ i < j ∧ j ≤ i + n→i(# vals0) ∨ r -- j ' ∈ st, ∀ r0, j0, i0, st0. r0 -- j0 ' ∈ putArray(vals0, r0, i0, st0) ↔ r0 -- j0 ' ∈ st0 ∨ i0 ≤ j0 ∧ j0 < i0 + n→i(# vals0) ⊦ r -- j ' ∈ putArray(vals0, r, i + 1, st) ↔ r -- j ' ∈ st ∨ ¬ n→i(# vals0) + i < j ∧ ¬ j < i, j = i

User applied rule case distinction

And closed the goal!

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≠ i0 → (¬ i < i0 ↔ i0 < i)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]