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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