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Proof step 28 from proof union-addarray-rew (previous step)

i < n→i(# vals), newref(r0, st0), newref(r0, st), 0 ≤ i ⊦ r0 = jvmref, vals = [], vals[i→n(i)] = (st ∪ addarray(r0, ty, vals, st0))[r0 -- i ']

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ rk ∈ st0 → (st ∪ st0)[rk] = st0[rk]
Proof step 26:
⊦ r -- j ' ∈ addarray(r, ty, vals, st) ↔ r -- j ' ∈ st ∨ 0 ≤ j ∧ j < n→i(# vals)
Proof step 27:
⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st)[r -- i ']) = vals[i→n(i)]

Rule argument

[speclemmaarg: ,rk ∈ st0 → (st ∪ st0)[rk] = st0[rk] ,[rk, st0, st] → [r0 -- i ', addarray(r0, ty, vals, st0), st] ,F ,storefunsx , ,union-at-right-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk]], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (r0 -- i ', addarray(r0, ty, vals, st0), st)]]