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Proof step 4 from proof getarray-union-01 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

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

Rule argument

[LEMMAARG : getarray-union-02, [r, st, j, st0] → [r, st, st[r -- _length] .intval, st0]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r, st, st[r -- _length] .intval, st0)]]