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Proof step 21 from proof validrefs-del-junkrefs (previous step)

is_obj(str, r0, st), junkrefs(str, r0 ' + r ', ty, st -- r), st[r0 -- _type] .type ≤ ty ⊦ r0 = jvmref, r = r0, junkref(str, r0, st), ∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ r = st[r0 -- fs '] .refval ∧ validrefs(str, st[r0 -- fs '] .refval ', fs .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 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 20:
is_obj(str, r0, st -- r) ∧ (st -- r)[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), r ' ≠ [] ∧ (∃ fs. fs ' ∈ instfields((st -- r)[r0 -- _type] .type .class) ∧ is_referencevalue((st -- r)[r0 -- fs ']) ∧ r ' .first = (st -- r)[r0 -- fs '] .refval ∧ junkrefs(str, r ', fs .type, st -- r)), st[r0 -- _type] .type ≤ ty ⊦ r0 = jvmref, r = r0, junkref(str, r0, st), ∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ r = st[r0 -- fs '] .refval ∧ validrefs(str, st[r0 -- fs '] .refval ', fs .type, 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 -- r, ty, r ', r0, str] ,F ,junkrefs , ,junkrefs-class ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( is_obj(str, r0, st -- r) ↔ is_obj(str, r0, st))], [CSIMPSEQ : ⊦ r ≠ r0 → (st -- r)[r0 -- sk0] = st[r0 -- sk0]])], [EXTRATERMS : (st -- r, ty, r ', r0, str)]]