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Proof step 40 from proof junkref-subspec-samesubclasses (previous step)

is_obj(str0, r, st), junkrefs(str, r ' + refs0, st[r -- _type] .type, st), same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0), ∀ str0, str, r, st, refs. # refs < # refs0 → ( same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0) ∧ junkrefs(str, r ' + refs, st[r -- _type] .type, st) → junkref(str0, r, st)) ⊦ r = jvmref, junkref(str0, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ junkrefs(str, refs, fs .type, st)))
Proof step 5:
⊦ ¬ is_obj(str, r, st) ∧ is_obj(str0, r, st) → ¬ same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0)
Proof step 39:
is_obj(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, is_obj(str0, r, st), refs0 ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs0 .first = st[r -- fs '] .refval ∧ junkrefs(str, refs0, fs .type, st)), same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0), ∀ str0, str, r, st, refs. # refs < # refs0 → ( same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0) ∧ junkrefs(str, r ' + refs, st[r -- _type] .type, st) → junkref(str0, r, st)) ⊦ r = jvmref, junkref(str0, r, st)

Rule argument

[speclemmaarg: , is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ junkrefs(str, refs, fs .type, st))) ,[st, ty, refs, r, str] → [st, st[r -- _type] .type, refs0, r, str] ,F ,junkrefs , ,junkrefs-class ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ ty])], [EXTRATERMS : (st, st[r -- _type] .type, refs0, r, str)]]