Nuprl Lemma : ss-comp_wf
∀[X,Y,Z:SeparationSpace]. ∀[f:Point(Y ⟶ Z)]. ∀[g:Point(X ⟶ Y)]. (ss-comp(f;g) ∈ Point(X ⟶ Z))
Proof
Definitions occuring in Statement :
ss-comp: ss-comp(f;g),
ss-fun: X ⟶ Y,
ss-point: Point(ss),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
guard: {T},
implies: P ⇒ Q,
compose: f o g,
all: ∀x:A. B[x],
ss-function: ss-function(X;Y;f),
ss-comp: ss-comp(f;g),
prop: ℙ,
top: Top,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
ss-eq_wf,
compose_wf,
separation-space_wf,
ss-fun_wf,
ss-point_wf,
ss-function_wf,
ss-fun-point
Rules used in proof :
independent_functionElimination,
dependent_functionElimination,
applyEquality,
lambdaFormation,
because_Cache,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesisEquality,
dependent_set_memberEquality,
rename,
setElimination,
sqequalRule,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
thin,
isectElimination,
extract_by_obid,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X,Y,Z:SeparationSpace]. \mforall{}[f:Point(Y {}\mrightarrow{} Z)]. \mforall{}[g:Point(X {}\mrightarrow{} Y)]. (ss-comp(f;g) \mmember{} Point(X {}\mrightarrow{} Z))
Date html generated:
2018_07_29-AM-10_12_03
Last ObjectModification:
2018_07_04-PM-11_33_51
Theory : constructive!algebra
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