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Proof step 49 from proof union-addarray-rew (previous step)

newref(r0, st0), newref(r0, st) ⊦ st[r0 -- fs '] = (st ∪ addarray(r0, ty, vals, st0))[r0 -- fs '], fs ' = _length, fs ' = _type, r0 = jvmref, r0 -- fs ' ∈ st0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ ¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk]
Proof step 47:
fs ' ≠ _type, fs ' ≠ _length ⊦ (addarray(r0, ty, vals, st)[r -- fs ']) = st[r -- fs ']
Proof step 48:
fs ' ≠ _type, fs ' ≠ _length ⊦ r -- fs ' ∈ addarray(r0, ty, vals, st) ↔ r -- fs ' ∈ st

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk ∈ st0 → (st ∪ st0)[rk] = st0[rk]], [CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st])], [EXTRATERMS : (r0 -- fs ', addarray(r0, ty, vals, st0), st)]]