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Proof step 16 from proof getarray-union-03 (conclusion)

⊦ r -- _length ∈ st ∧ 0 ≤ i ∧ j ≤ st[r -- _length] .intval - i ∧ (∀ i1. i ≤ i1 ∧ i1 < i + j → r -- i1 ' ∈ st) → getarray(r, i, j, st0 ∪ st) = getarray(r, i, j, st)

User applied rule induction

And obtained the following new goals

Proof step 15:
true, ∀ st0, i, st, r, j0. i→n(j0) < i→n(j) → ( true → ( r -- _length ∈ st ∧ 0 ≤ i ∧ j0 ≤ st[r -- _length] .intval - i ∧ (∀ i1. i ≤ i1 ∧ i1 < i + j0 → r -- i1 ' ∈ st) → getarray(r, i, j0, st0 ∪ st) = getarray(r, i, j0, st))) ⊦ r -- _length ∈ st ∧ 0 ≤ i ∧ j ≤ st[r -- _length] .intval - i ∧ (∀ i1. i ≤ i1 ∧ i1 < i + j → r -- i1 ' ∈ st) → getarray(r, i, j, st0 ∪ st) = getarray(r, i, j, st)

Rule argument

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

Additional information

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