Nuprl Lemma : ss-const_wf
∀[X,Y:SeparationSpace]. ∀[c:Point(Y)]. (ss-const(c) ∈ Point(X ⟶ Y))
Proof
Definitions occuring in Statement :
ss-const: ss-const(c),
ss-fun: X ⟶ Y,
ss-point: Point(ss),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
prop: ℙ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
ss-function: ss-function(X;Y;f),
ss-const: ss-const(c),
top: Top,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
separation-space_wf,
ss-function_wf,
ss-eq_wf,
ss-eq_weakening,
ss-point_wf,
ss-fun-point
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
lambdaFormation,
hypothesisEquality,
lambdaEquality,
dependent_set_memberEquality,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X,Y:SeparationSpace]. \mforall{}[c:Point(Y)]. (ss-const(c) \mmember{} Point(X {}\mrightarrow{} Y))
Date html generated:
2018_07_29-AM-10_12_08
Last ObjectModification:
2018_07_06-PM-02_11_57
Theory : constructive!algebra
Home
Index