Nuprl Lemma : ss-homotopic_wf
∀[X:SeparationSpace]. ∀[x0,x1:Point(X)]. ∀[a,b:Point(Path(X))]. (ss-homotopic(X;x0;x1;a;b) ∈ ℙ)
Proof
Definitions occuring in Statement :
ss-homotopic: ss-homotopic(X;x0;x1;a;b),
path-ss: Path(X),
ss-point: Point(ss),
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,
ss-homotopic: ss-homotopic(X;x0;x1;a;b),
all: ∀x:A. B[x],
top: Top,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
guard: {T},
so_apply: x[s]
Lemmas referenced :
member_rccint_lemma,
exists_wf,
ss-point_wf,
path-ss_wf,
ss-eq_wf,
path-at_wf,
rleq_weakening_equal,
int-to-real_wf,
rleq-int,
false_wf,
rleq_wf,
all_wf,
real_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
hypothesisEquality,
lambdaEquality,
productEquality,
because_Cache,
natural_numberEquality,
independent_isectElimination,
independent_pairFormation,
productElimination,
independent_functionElimination,
lambdaFormation,
dependent_set_memberEquality,
setEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[X:SeparationSpace]. \mforall{}[x0,x1:Point(X)]. \mforall{}[a,b:Point(Path(X))]. (ss-homotopic(X;x0;x1;a;b) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-PM-01_20_33
Last ObjectModification:
2018_07_05-PM-03_51_35
Theory : intuitionistic!topology
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