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Proof step 26 from proof exvalidrefs-03 (previous step)

st[r -- _type] .type = mkclasstype(class1), st[r -- mkfs(class0, mkclasstype(class2), fieldvar) '] = refval(r0), class1 ≤ class, class2 ≤ class, mkfs(class0, mkclasstype(class2), fieldvar) ' ∈ instfields(class), is_obj(str, r, st), st[r0 -- _type] .type ≤ mkclasstype(class2), st[r0 -- _type] .type ≤ mkclasstype(class), junkrefs(str, (r0 ' + refs) + r ', st[r0 -- _type] .type, st -- r), is_obj(str, r0, st), class1 ≤ class2, ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st0[r -- _type] .type ≤ fs .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r = r0, r = jvmref, r0 = jvmref, r ∈ refs, junkref(str, r0, st), validrefs(str, r0 ' + refs + r ', mkclasstype(class2), st), junkrefs(str, (r0 ' + refs) + r ', mkclasstype(class2), st -- r), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , junkrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ st[r -- _type] .type ≤ ty ∧ r ≠ jvmref → junkrefs(str, r ' + refs, ty, st) ,[st, ty, refs, r, str] → [st -- r, mkclasstype(class2), refs + r ', r0, str] ,F ,junkrefs , ,junkrefs-sametype-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → (st -- r)[r0 -- sk0] = st[r0 -- sk0]], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st -- r, mkclasstype(class2), refs + r ', r0, str)]]