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Proof step 9 from proof getarray-union (previous step)

0 ≤ i0, ∀ st0, st, i, r, j0. i→n(j0) < i→n(i0 + 1) → (true → getarray(r, i, j0, st ∪ st0) = getarray(r, i, j0, st0) ∨ r ∈ st) ⊦ (st ∪ st0)[r -- i '] ' + getarray(r, i + 1, i0, st ∪ st0) = getarray(r, i, i0 + 1, st0), r ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ rk ∈ st → (st ∪ st0)[rk] = st0[rk]
Proof step 8:
¬ r -- i ' ∈ st, 0 ≤ i0, ∀ st0, st, i, r, j0. i→n(j0) < i→n(i0 + 1) → (true → getarray(r, i, j0, st ∪ st0) = getarray(r, i, j0, st0) ∨ r ∈ st) ⊦ st0[r -- i '] ' + getarray(r, i + 1, i0, st ∪ st0) = getarray(r, i, i0 + 1, st0), r ∈ st

Rule argument

[speclemmaarg: ,¬ rk ∈ st → (st ∪ st0)[rk] = st0[rk] ,[rk, st0, st] → [r -- i ', st0, st] ,F ,storefunsx , ,union-at-right-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st])], [EXTRATERMS : (r -- i ', st0, st)]]