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Proof step 6 from proof putArray-in (previous step)

sk = i0 ', 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 < i0 ∧ i0 ≤ i + n→i(# vals0) ∨ sk = i ' ⊦ r -- sk ∈ st, ¬ n→i(# vals0) + i < i0 ∧ ¬ i0 < i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
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

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ is_indexkey(i ')])]]