Nuprl Lemma : dlattice-eq-equiv
∀[X:Type]. EquivRel(X List List;as,bs.dlattice-eq(X;as;bs))
Proof
Definitions occuring in Statement :
dlattice-eq: dlattice-eq(X;as;bs),
list: T List,
equiv_rel: EquivRel(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
dlattice-eq: dlattice-eq(X;as;bs),
cand: A c∧ B,
member: t ∈ T,
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
prop: ℙ,
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
list_wf,
dlattice-order_wf,
dlattice-order_weakening,
dlattice-order_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
lambdaFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
sqequalRule,
productElimination,
productEquality,
because_Cache,
universeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[X:Type]. EquivRel(X List List;as,bs.dlattice-eq(X;as;bs))
Date html generated:
2020_05_20-AM-08_26_44
Last ObjectModification:
2017_01_21-PM-04_06_14
Theory : lattices
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