Nuprl Lemma : ss-homeo_transitivity
∀[X,Y,Z:SeparationSpace]. (ss-homeo(X;Y) ⇒ ss-homeo(Y;Z) ⇒ ss-homeo(X;Z))
Proof
Definitions occuring in Statement :
ss-homeo: ss-homeo(X;Y),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
ss-homeo: ss-homeo(X;Y),
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
ss-comp: ss-comp(f;g),
ss-ap: f(x),
compose: f o g,
cand: A c∧ B,
ss-eq: x ≡ y,
not: ¬A,
false: False,
guard: {T},
uimplies: b supposing a,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
ss-comp_wf,
all_wf,
ss-point_wf,
ss-eq_wf,
ss-ap_wf,
exists_wf,
ss-fun_wf,
ss-homeo_wf,
separation-space_wf,
ss-sep_wf,
ss-eq_functionality,
ss-ap_functionality,
ss-eq_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
productEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
voidElimination,
independent_pairFormation,
because_Cache,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[X,Y,Z:SeparationSpace]. (ss-homeo(X;Y) {}\mRightarrow{} ss-homeo(Y;Z) {}\mRightarrow{} ss-homeo(X;Z))
Date html generated:
2020_05_20-PM-01_19_59
Last ObjectModification:
2018_07_04-PM-11_38_46
Theory : intuitionistic!topology
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