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Proof step 4 from proof getarray-union-02 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
⊦ 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)
Proof step 3:
r -- _length ∈ st ∧ 0 ≤ 0 ∧ j ≤ st[r -- _length] .intval - 0 ∧ (∀ i1. 0 ≤ i1 ∧ i1 < 0 + j → r -- i1 ' ∈ st) → getarray(r, 0, j, st0 ∪ st) = getarray(r, 0, j, st), r -- _length ∈ st, j ≤ st[r -- _length] .intval, r ∈ st, 0 < j, 0 < st[r -- _length] .intval, ∀ i. ¬ i < 0 ∧ ¬ j ≤ i → r -- i ' ∈ st ⊦ getarray(r, 0, j, st0 ∪ st) = getarray(r, 0, j, st)

Rule argument

[LEMMAARG : getarray-union-03, [r, st, i, j, st0] → [r, st, 0, j, st0]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r, st, 0, j, st0)]]