Nuprl Lemma : uand-subtype2
∀[A,B:Type]. (uand(A;B) ⊆r B)
Proof
Definitions occuring in Statement :
uand: uand(A;B),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uand: uand(A;B),
has-value: (a)↓,
prop: ℙ
Lemmas referenced :
uand_wf,
has-value_wf_base,
is-exception_wf,
sqle_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
sqequalRule,
extract_by_obid,
hypothesisEquality,
hypothesis,
axiomEquality,
universeEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyEquality,
divergentSqle,
sqleReflexivity,
rename,
isectEquality
Latex:
\mforall{}[A,B:Type]. (uand(A;B) \msubseteq{}r B)
Date html generated:
2019_06_20-AM-11_29_56
Last ObjectModification:
2018_08_21-AM-00_02_26
Theory : per!type
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