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Proof step 12 from proof isobj-addobj-02 (previous step)

⊦ r = r0, r ≠ jvmref ∧ r -- _type ∈ addobj(r0, class, fis, st) ∧ is_typevalue(addobj(r0, class, fis, st)[r -- _type]) ∧ is_classtype((addobj(r0, class, fis, st)[r -- _type]) .type) ∧ is_obj(r, (addobj(r0, class, fis, st)[r -- _type]) .type .class, addobj(r0, class, fis, st)) ↔ is_obj(r, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ r ≠ r0 → (r -- sk ∈ addobj(r0, class1, fis, st) ↔ r -- sk ∈ st)
Proof step 3:
⊦ r ≠ r0 → (addobj(r, class1, fis, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 4:
⊦ r ≠ r0 → (is_obj(r, class0, addobj(r0, class, fis, st)) ↔ is_obj(r, class0, st))
Proof step 5:
⊦ ¬ is_obj(r, st) → ¬ is_obj(r, class, st)
Proof step 6:
⊦ ¬ is_obj(jvmref, st)
Proof step 7:
⊦ ¬ r -- _type ∈ st → ¬ is_obj(r, st)
Proof step 8:
⊦ ¬ is_typevalue(st[r -- _type]) → ¬ is_obj(r, st)
Proof step 9:
⊦ ¬ is_classtype(st[r -- _type] .type) → ¬ is_obj(r, st)
Proof step 11:
is_obj(r, st), is_classtype(st[r -- _type] .type), is_typevalue(st[r -- _type]), r -- _type ∈ st, r ∈ st ⊦ r = r0, r = jvmref, is_obj(r, st[r -- _type] .type .class, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st])]]