Nuprl Lemma : worlds_wf
∀[k:dl_KripkeStructure]. (worlds(k) ∈ Type)
Proof
Definitions occuring in Statement :
dl_KripkeStructure: dl_KripkeStructure,
worlds: worlds(k),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dl_KripkeStructure: dl_KripkeStructure,
worlds: worlds(k),
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
subtype_rel_self,
record-select_wf,
top_wf,
istype-atom,
nat_wf,
dl_KripkeStructure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
dependentIntersectionElimination,
dependentIntersectionEqElimination,
thin,
hypothesis,
applyEquality,
tokenEquality,
instantiate,
extract_by_obid,
isectElimination,
universeEquality,
functionEquality,
cumulativity,
lambdaEquality_alt,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
universeIsType
Latex:
\mforall{}[k:dl\_KripkeStructure]. (worlds(k) \mmember{} Type)
Date html generated:
2020_05_20-AM-09_01_12
Last ObjectModification:
2019_11_27-PM-01_59_11
Theory : dynamic!logic
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