Nuprl Lemma : path-at_functionality
∀[X:SeparationSpace]. ∀[p:Point(Path(X))]. ∀[t,t':{t:ℝ| t ∈ [r0, r1]} ]. p@t ≡ p@t' supposing t = t'
Proof
Definitions occuring in Statement :
path-at: p@t,
path-ss: Path(X),
ss-eq: x ≡ y,
ss-point: Point(ss),
separation-space: SeparationSpace,
rccint: [l, u],
i-member: r ∈ I,
req: x = y,
int-to-real: r(n),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
top: Top,
path-at: p@t,
all: ∀x:A. B[x],
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
ss-eq: x ≡ y,
not: ¬A,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q
Lemmas referenced :
path-ss-point,
sq_stable__ss-eq,
member_rccint_lemma,
ss-sep_wf,
path-at_wf,
req_wf,
set_wf,
real_wf,
i-member_wf,
rccint_wf,
int-to-real_wf,
ss-point_wf,
path-ss_wf,
separation-space_wf,
unit-ss-eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
setElimination,
rename,
hypothesisEquality,
applyEquality,
sqequalRule,
dependent_functionElimination,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
lambdaEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
productElimination,
independent_isectElimination
Latex:
\mforall{}[X:SeparationSpace]. \mforall{}[p:Point(Path(X))]. \mforall{}[t,t':\{t:\mBbbR{}| t \mmember{} [r0, r1]\} ]. p@t \mequiv{} p@t' supposing t = t\000C'
Date html generated:
2020_05_20-PM-01_20_17
Last ObjectModification:
2018_07_03-PM-05_13_04
Theory : intuitionistic!topology
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