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Proof step 20 from proof maxpath-object (previous step)

st[r -- fs '] = refval(r0), maxpath(str, r, st) = 1, 1 ≤ maxpath(str, r0, st), validrefs(str, r ', st[r -- _type] .type, st), fs ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st) ⊦ validrefset(str, r, st) = ∅, # validrefset(str, r, st) = 0, maxpath(str, r0, st) = 0, junkref(str, r, st), cyclic(str, r, st), has_reffield(r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ is_obj(r, st) → (has_reffield(r, st) ↔ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_reftype(fs .type)))
Proof step 19:
is_obj(r, st), st[r -- fs '] = refval(r0), maxpath(str, r, st) = 1, 1 ≤ maxpath(str, r0, st), validrefs(str, r ', st[r -- _type] .type, st), fs ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st) ⊦ validrefset(str, r, st) = ∅, # validrefset(str, r, st) = 0, maxpath(str, r0, st) = 0, junkref(str, r, st), cyclic(str, r, st), ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_reftype(fs .type)

Rule argument

[speclemmaarg: , is_obj(r, st) → ( has_reffield(r, st) ↔ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_reftype(fs .type))) ,[st, r] → [st, r] ,F ,addfuns , ,has_reffield-class ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_obj(r, st) → ¬ is_obj(str, r, st)])], [EXTRATERMS : (st, r)]]