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