Nuprl Lemma : free-dl-generator_wf
∀[X:Type]. ∀[x:X]. (free-dl-generator(x) ∈ free-dl-type(X))
Proof
Definitions occuring in Statement :
free-dl-generator: free-dl-generator(x),
free-dl-type: free-dl-type(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
free-dl-generator: free-dl-generator(x),
subtype_rel: A ⊆r B,
free-dl-type: free-dl-type(X),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
cons_wf,
list_wf,
nil_wf,
subtype_quotient,
dlattice-eq_wf,
dlattice-eq-equiv
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[x:X]. (free-dl-generator(x) \mmember{} free-dl-type(X))
Date html generated:
2020_05_20-AM-08_27_34
Last ObjectModification:
2017_01_22-PM-07_46_48
Theory : lattices
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