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Proof step 30 from proof getintarray-in (previous step)

⊦ (∃ n. n < # 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)

User applied rule case distinction

And obtained the following new goals

Proof step 18:
∃ n. n < # 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
Proof step 29:
∃ j. i = st[r -- j '] .intval ∧ ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j ⊦ ∃ n. n < # getarray(r, 0, st[r -- _length] .intval, st) ∧ (intvalues(getarray(r, 0, st[r -- _length] .intval, st))[n]) = i

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]