Nuprl Lemma : ss-id_wf
∀[X:SeparationSpace]. (ss-id() ∈ Point(X ⟶ X))
Proof
Definitions occuring in Statement :
ss-id: ss-id(),
ss-fun: X ⟶ Y,
ss-point: Point(ss),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
implies: P ⇒ Q,
all: ∀x:A. B[x],
ss-function: ss-function(X;Y;f),
ss-id: ss-id(),
prop: ℙ,
top: Top,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
ss-eq_wf,
ss-point_wf,
ss-fun-point,
ss-function_wf,
separation-space_wf
Rules used in proof :
lambdaFormation,
lambdaEquality,
hypothesisEquality,
thin,
isectElimination,
dependent_set_memberEquality,
voidEquality,
voidElimination,
isect_memberEquality,
extract_by_obid,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
sqequalRule,
hypothesis,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X:SeparationSpace]. (ss-id() \mmember{} Point(X {}\mrightarrow{} X))
Date html generated:
2018_07_29-AM-10_11_56
Last ObjectModification:
2018_07_04-PM-00_20_46
Theory : constructive!algebra
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