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Proof step 40 from proof exvalidrefs-03 (previous step)

st[r -- mkfs(class0, ty, fieldvar) '] = refval(r0), st[r0 -- _type] .type ≤ ty, is_classtype(st[r -- _type] .type), is_obj(str, r, st), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), ty ≤ mkclasstype(class), st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ mkclasstype(class), is_obj(str, r0, st), junkrefs(str, r0 ' + refs0, st[r0 -- _type] .type, st -- r), st[r0 -- _type] .type ≤ mkclasstype(class), r ∈ refs0, ∀ 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)) ⊦ r0 = jvmref, r = jvmref, r = r0, junkref(str, r0, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref, ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,r ∈ refs → (∃ refs0, refs1. refs = refs0 + r ' + refs1 ∧ ¬ r ∈ refs0) ,[r, refs] → [r, refs0] ,F ,list ,references-olista ,firstoc ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r, refs0)]]