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Proof step 9 from proof putArray-in (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 8:
is_indexkey(sk), r -- sk ∈ putArray(vals0, r, i + 1, st[r -- i ', val]), r ∈ putArray(vals0, r, i + 1, st[r -- i ', val]), sk = i ' ∨ is_indexkey(sk) ∧ i < sk .index ∧ sk .index ≤ i + n→i(# vals0), ∀ 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) ⊦ r -- sk ∈ st, ¬ n→i(# vals0) + i < sk .index ∧ ¬ sk .index < i ∧ ¬ is_fskey(sk)

Rule argument

[fma-arg: is_indexkey(sk)]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ is_fskey(i ')], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)])], [EXTRAFMAS : (is_indexkey(sk))]]