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Proof step 32 from proof getintarray-in (previous step)

⊦ i ∈ intvalues(getarray(r, 0, st[r -- _length] .intval, st)) ↔ (∃ j. i = st[r -- j '] .intval ∧ ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i ∈ ints ↔ (∃ n. n < # ints ∧ ints[n] = i)
Proof step 31:
⊦ (∃ n. n < # intvalues(getarray(r, 0, st[r -- _length] .intval, st)) ∧ (intvalues(getarray(r, 0, st[r -- _length] .intval, st))[n]) = i) ↔ (∃ j. i = st[r -- j '] .intval ∧ ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j)

Rule argument

[speclemmaarg: ,i ∈ ints ↔ (∃ n. n < # ints ∧ ints[n] = i) ,[ints, i] → [intvalues(getarray(r, 0, st[r -- _length] .intval, st)), i] ,F ,list-del ,intlista ,in-get ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (intvalues (getarray(r, 0, st[r -- _length] .intval, st)), i)]]