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Proof step 6 from proof is_array-union-disjoint (previous step)

st1 .refs ∩ st .refs = ∅, r ∈ st, is_array(r, st1), type∃(str, st1[r -- _type] .type), r ∈ st1, r -- _type ∈ st, r ∈ st .refs, ¬ type∃(str, st[r -- _type] .type) ∨ st[r -- _type] .type .jtelemtype = void_type ∨ st[r -- _type] .type .jtelemtype = abstract_type ⊦ st1[r -- _type] .type .jtelemtype = abstract_type, st1[r -- _type] .type .jtelemtype = void_type, st = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ r ∈ st ↔ r ∈ st .refs

Rule argument

[speclemmaarg: ,r ∈ st ↔ r ∈ st .refs ,[st, r] → [st1, r] ,F ,storefunsx , ,instore-inrefs ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (rset ∩ rset0) ∩ rset1 = rset ∩ rset0 ∩ rset1], [CSIMPSEQ : ⊦ rset ∩ rset0 = rset0 ∩ rset], [CSIMPSEQ : ⊦ rset ∩ rset0 = ∅ ∧ r ∈ rset → (¬ ¬ r ∈ rset0 ↔ false)])], [EXTRATERMS : (st1, r)]]