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Proof step 141 from proof putarray-addarray-01 (previous step)

0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, r -- i0 ' ∈ putArray(vals, r, i, addarray(r, ty, j, st)), i0 < 0 ∨ i + n→i(# vals) ≤ i0 ⊦ r -- i0 ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 136:
⊦ rk ∈ putArray(vals, r, i, st) ↔ rk ∈ st ∨ rk .ref = r ∧ is_indexkey(rk .key) ∧ i ≤ rk .key .index ∧ rk .key .index < i + n→i(# vals)
Proof step 140:
0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, r -- i0 ' ∈ addarray(r, ty, j, st) ∨ (r -- i0 ') .ref = r ∧ is_indexkey((r -- i0 ') .key) ∧ i ≤ (r -- i0 ') .key .index ∧ (r -- i0 ') .key .index < i + n→i(# vals), i0 < 0 ∨ i + n→i(# vals) ≤ i0 ⊦ r -- i0 ' ∈ st

Rule argument

[speclemmaarg: , rk ∈ putArray(vals, r, i, st) ↔ rk ∈ st ∨ rk .ref = r ∧ is_indexkey(rk .key) ∧ i ≤ rk .key .index ∧ rk .key .index < i + n→i(# vals) ,[st, i, r, vals, rk] → [addarray(r, ty, j, st), i, r, vals, r -- i0 '] ,F ,storearrays , ,putArray-in ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r, ty, j, st), i, r, vals, r -- i0 ')]]