from relations import W, build_relations
from ext import attach
def exts(L, gens=("cap","T","X")):
    return [attach(L,i,g) for g in gens for i in range(L.k)]
def proof_hosts(t, level=6):
    rels=build_relations(t); R={r["name"]:r for r in rels}
    L2=R["R2"]["L"]; L25=R["R25"]["L"]; L3=R["R3"]["L"]
    h = exts(L2,("cap","T"))
    if level>=5: h += exts(L25,("cap","T","X"))
    if level>=6: h += exts(L3,("cap","T","X"))
    return h