Nuprl Lemma : inclusion-partial2
∀[T:Type]. ∀x:T. (x ∈ partial(T)) supposing value-type(T)
Proof
Definitions occuring in Statement :
partial: partial(T),
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
inclusion-partial,
value-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
hypothesisEquality,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
independent_isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}x:T. (x \mmember{} partial(T)) supposing value-type(T)
Date html generated:
2016_05_14-AM-06_09_32
Last ObjectModification:
2015_12_26-AM-11_52_22
Theory : partial_1
Home
Index