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Proof step 166 from proof compat-addclass (previous step)

fis .keys = statfields(class), st[r -- _type] = typeval(ty), r ∈ st, okfieldinits(class, fis), compatrefs(str, st), compatstatic(str, st), compatmode(str, st), r -- _type ∈ addclass(class, fis, st) ⊦ r = jvmref, (is_classtype(ty) ∧ class+∃(str, ty .class) → compatobj(str, r, addclass(class, fis, st))) ∧ (is_arraytype(ty) ∧ (¬ has_classtype(ty) ∨ tdname+∃(str, ty .type .jtelemtype .class)) → compatarray(str, r, addclass(class, fis, st)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 130:
⊦ 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 165:
fis .keys = statfields(class), st[r -- _type] = typeval(ty), r ∈ st, okfieldinits(class, fis), ∀ 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)), compatstatic(str, st), compatmode(str, st), r -- _type ∈ addclass(class, fis, st) ⊦ r = jvmref, (is_classtype(ty) ∧ class+∃(str, ty .class) → compatobj(str, r, addclass(class, fis, st))) ∧ (is_arraytype(ty) ∧ (¬ has_classtype(ty) ∨ tdname+∃(str, ty .type .jtelemtype .class)) → compatarray(str, r, addclass(class, fis, st)))

Rule argument

[crewrite-arg: refs-compat, F, [st, str] → [st, str]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, str)]]