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Proof step 143 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)), r ∈ 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 134:
⊦ r1 ∈ putArray(vals, r0, i0, st) ↔ r1 ∈ st ∨ r1 = r0 ∧ vals ≠ []
Proof step 142:
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)), r ∈ addarray(r, ty, j, st) ∨ r = r ∧ vals ≠ [], i0 < 0 ∨ i + n→i(# vals) ≤ i0 ⊦ r -- i0 ' ∈ st

Rule argument

[speclemmaarg: ,r1 ∈ putArray(vals, r0, i0, st) ↔ r1 ∈ st ∨ r1 = r0 ∧ vals ≠ [] ,[st, i0, r0, vals, r1] → [addarray(r, ty, j, st), i, r, vals, r] ,F ,storearrays , ,putar-in ]

Additional information

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