Nuprl Lemma : flattice-order_wf
∀[X:Type]. ∀[as,bs:(X + X) List List]. (flattice-order(X;as;bs) ∈ ℙ)
Proof
Definitions occuring in Statement :
flattice-order: flattice-order(X;as;bs),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
flattice-order: flattice-order(X;as;bs),
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
l_all_wf2,
list_wf,
l_member_wf,
or_wf,
l_exists_wf,
equal_wf,
flip-union_wf,
l_contains_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
setEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[as,bs:(X + X) List List]. (flattice-order(X;as;bs) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-08_59_15
Last ObjectModification:
2017_01_24-AM-10_47_56
Theory : lattices
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