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Proof step 17 from proof getarray-in-01 (previous step)

val ∈ getarray(r, i0, i1, st), 0 < i1 ⊦ ∃ i. ¬ i < i0 ∧ ¬ i0 + i1 ≤ i ∧ st[r -- i '] = val

User applied rule induction

And obtained the following new goals

Proof step 16:
val ∈ getarray(r, i0, i1, st) ∧ 0 < i1, ∀ st, i0, r, val, i. i→n(i) < i→n(i1) → (val ∈ getarray(r, i0, i, st) ∧ 0 < i → (∃ i2. ¬ i2 < i0 ∧ ¬ i0 + i ≤ i2 ∧ st[r -- i2 '] = val)) ⊦ ∃ i. ¬ i < i0 ∧ ¬ i0 + i1 ≤ i ∧ st[r -- i '] = val

Rule argument

[INDHYPARG : [STANDARDINDUCTIONTYPE : ], true, false, i→n(i1), [] → [], <]

Additional information

[[CONCRETESIMPRULES : ([CSIMPLESSPRED : <])], [EXTRATERMS : (i→n(i1))]]