Nuprl Lemma : K-struct_wf
∀[K:mKripkeStruct]. ∀[i:World].  (K-struct(K;i) ∈ FOStruct(Dom(i)))
Proof
Definitions occuring in Statement : 
K-struct: K-struct(K;i)
, 
K-dom: Dom(i)
, 
K-world: World
, 
mFO-Kripke-struct: mKripkeStruct
, 
FOStruct: FOStruct(Dom)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
mFO-Kripke-struct: mKripkeStruct
, 
spreadn: spread4, 
K-struct: K-struct(K;i)
, 
K-dom: Dom(i)
, 
pi1: fst(t)
, 
pi2: snd(t)
, 
subtype_rel: A ⊆r B
, 
and: P ∧ Q
, 
K-world: World
Lemmas referenced : 
subtype_rel_self, 
K-world_wf, 
mFO-Kripke-struct_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
sqequalHypSubstitution, 
productElimination, 
thin, 
sqequalRule, 
applyEquality, 
hypothesisEquality, 
extract_by_obid, 
isectElimination, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeIsType, 
isect_memberEquality_alt, 
isectIsTypeImplies, 
inhabitedIsType
Latex:
\mforall{}[K:mKripkeStruct].  \mforall{}[i:World].    (K-struct(K;i)  \mmember{}  FOStruct(Dom(i)))
Date html generated:
2019_10_16-AM-11_44_48
Last ObjectModification:
2018_10_13-AM-11_57_46
Theory : minimal-first-order-logic
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