Nuprl Lemma : iPO_wf
∀[K:dl_KripkeStructure]. ∀[s,t:worlds(K)]. (iPO(K;s;t) ∈ ℙ)
Proof
Definitions occuring in Statement :
dl_KripkeStructure: dl_KripkeStructure,
iPO: iPO(k;s;t),
worlds: worlds(k),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
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,
iPO: iPO(k;s;t)
Lemmas referenced :
subtype_rel_self,
record-select_wf,
top_wf,
istype-atom,
nat_wf,
worlds_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,
hypothesisEquality,
axiomEquality,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[K:dl\_KripkeStructure]. \mforall{}[s,t:worlds(K)]. (iPO(K;s;t) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-09_01_14
Last ObjectModification:
2019_11_27-PM-02_15_13
Theory : dynamic!logic
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