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Proof step 8 from proof putArray-in (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
is_indexkey(sk), r -- sk ∈ 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), i < sk .index ∧ sk .index ≤ i + n→i(# vals0) ∨ sk = i ' ⊦ r -- sk ∈ st, ¬ n→i(# vals0) + i < sk .index ∧ ¬ sk .index < i

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)])]]