| ¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty)), validrefs(str, r ' + acc, ty, st), ty ≤ ty0, ∀ ty, ty0, str, st. ty ≤ ty0 ∧ validrefs(str, acc, ty, st) → validrefs(str, acc, ty0, st) ⊦ r = jvmref, validrefs(str, r ' + acc, ty0, st) |
validrefs(str, r ' + acc, ty, st), ty ≤ ty0, is_valid_ref(str, r, st), st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty0, ∀ ty, ty0, str, st. ty ≤ ty0 ∧ validrefs(str, acc, ty, st) → validrefs(str, acc, ty0, st) ⊦ r = jvmref, validrefs(str, r ' + acc, ty0, st)
[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ ty ≤ ty0 ∧ ty0 ≤ ty1 → ty ≤ ty1], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]