⊦ validmode(str, st) ↔ _mode ∈ st ∧ validmode(str, st[_mode], st)
validmode(str, st), st ⊆ st0 ⊦ _mode ∈ st0 ∧ validmode(str, st0[_mode], st0)
[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, str)]]