Nuprl Lemma : face-lattice-constraints_wf
∀[T:Type]. ∀[x:T + T]. (face-lattice-constraints(x) ∈ fset(fset(T + T)))
Proof
Definitions occuring in Statement :
face-lattice-constraints: face-lattice-constraints(x),
fset: fset(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
face-lattice-constraints: face-lattice-constraints(x),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
fset-singleton_wf,
fset_wf,
fset-pair_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
because_Cache,
lambdaFormation,
unionElimination,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
unionEquality,
inlEquality,
inrEquality,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T + T]. (face-lattice-constraints(x) \mmember{} fset(fset(T + T)))
Date html generated:
2020_05_20-AM-08_50_35
Last ObjectModification:
2018_08_21-PM-02_01_38
Theory : lattices
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