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Proof step 187 from proof compat-addobj (previous step)

compatrefs(str, st), compatstatic(str, st), compatmode(str, st), newref(r, st), is_predefined_class(class) ⊦ compatrefs(str, addobj(r, class, [], st)), r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 105:
⊦ compatrefs(str, st) ↔ (∀ r. r ≠ jvmref ∧ r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) → (is_classtype(st[r -- _type] .type) ∧ class+∃(str, st[r -- _type] .type .class) → compatobj(str, r, st)) ∧ ( is_arraytype(st[r -- _type] .type) ∧ (¬ has_classtype(st[r -- _type] .type) ∨ tdname+∃(str, st[r -- _type] .type .jtelemtype .class)) → compatarray(str, r, st)))
Proof step 186:
compatrefs(str, st), compatstatic(str, st), compatmode(str, st), newref(r, st), is_predefined_class(class) ⊦ ∀ r0. r0 ≠ jvmref ∧ r0 -- _type ∈ addobj(r, class, [], st) ∧ is_typevalue(addobj(r, class, [], st)[r0 -- _type]) → ( is_classtype((addobj(r, class, [], st)[r0 -- _type]) .type) ∧ class+∃(str, (addobj(r, class, [], st)[r0 -- _type]) .type .class) → compatobj(str, r0, addobj(r, class, [], st))) ∧ ( is_arraytype((addobj(r, class, [], st)[r0 -- _type]) .type) ∧ ( ¬ has_classtype((addobj(r, class, [], st)[r0 -- _type]) .type) ∨ tdname+∃(str, (addobj(r, class, [], st)[r0 -- _type]) .type .jtelemtype .class)) → compatarray(str, r0, addobj(r, class, [], st))), r = jvmref

Rule argument

[crewrite-arg: refs-compat , F , [st, str] → [addobj(r, class, [], st), str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addobj(r, class, [], st), str)]]