Nuprl Lemma : path-comp-property_wf
∀[X:SeparationSpace]. (path-comp-property(X) ∈ ℙ)
Proof
Definitions occuring in Statement :
path-comp-property: path-comp-property(X),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
path-comp-property: path-comp-property(X),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
all_wf,
ss-point_wf,
path-ss_wf,
ss-eq_wf,
path-at_wf,
member_rccint_lemma,
rleq-int,
istype-false,
int-to-real_wf,
rleq_wf,
exists_wf,
path-comp-rel_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality_alt,
because_Cache,
functionEquality,
dependent_functionElimination,
Error :memTop,
natural_numberEquality,
productElimination,
independent_functionElimination,
independent_pairFormation,
lambdaFormation_alt,
dependent_set_memberEquality_alt,
productIsType,
universeIsType,
inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[X:SeparationSpace]. (path-comp-property(X) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-PM-01_20_46
Last ObjectModification:
2020_02_08-AM-11_41_36
Theory : intuitionistic!topology
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