Nuprl Lemma : uand-subtype1
∀[A,B:Type]. ∀[z:uand(A;B)]. (z ∈ A)
Proof
Definitions occuring in Statement :
uand: uand(A;B),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uand: uand(A;B),
has-value: (a)↓,
subtype_rel: A ⊆r B,
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,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
sqequalRule,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
hypothesisEquality,
isect_memberEquality,
because_Cache,
universeEquality,
applyEquality,
lambdaEquality,
divergentSqle,
sqleReflexivity,
rename,
isectEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[z:uand(A;B)]. (z \mmember{} A)
Date html generated:
2019_06_20-AM-11_29_54
Last ObjectModification:
2018_08_21-AM-00_01_19
Theory : per!type
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