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Proof step 12 from proof putArray-in (previous step)

r0 = r ∧ ¬ is_fskey(sk) ∧ ¬ sk .index < i ∧ ¬ n→i(# vals0) + i < sk .index ∨ r0 -- sk ∈ st, r0 -- sk ∈ putArray(vals0, r, i + 1, st[r -- i ', val]) ↔ r0 = r ∧ is_indexkey(sk) ∧ i < sk .index ∧ sk .index ≤ i + n→i(# vals0) ∨ r0 -- sk ∈ 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) ⊦ r0 -- sk ∈ putArray(vals0, r, i + 1, st[r -- i ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
is_indexkey(sk), ∀ 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) ⊦ sk = sk .index ', r -- sk ∈ st, r -- sk ∈ putArray(vals0, r, sk .index + 1, st[r -- sk .index ', val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ 0 ≤ n→i(n)], [CSIMPSEQ : ⊦ i ≤ i + j ↔ 0 ≤ j], [CSIMPFORWARD : ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)])]]