Nuprl Lemma : path-at_wf
∀[X:SeparationSpace]. ∀[p:Point(Path(X))]. ∀[t:{t:ℝ| t ∈ [r0, r1]} ]. (p@t ∈ Point(X))
Proof
Definitions occuring in Statement :
path-at: p@t,
path-ss: Path(X),
ss-point: Point(ss),
separation-space: SeparationSpace,
rccint: [l, u],
i-member: r ∈ I,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
path-at: p@t,
and: P ∧ Q,
prop: ℙ,
cand: A c∧ B,
i-member: r ∈ I,
rccint: [l, u],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
path-ss-point,
real_wf,
rleq_wf,
int-to-real_wf,
set_wf,
i-member_wf,
rccint_wf,
ss-point_wf,
path-ss_wf,
separation-space_wf
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,
sqequalRule,
applyEquality,
functionExtensionality,
hypothesisEquality,
setEquality,
productEquality,
natural_numberEquality,
because_Cache,
productElimination,
independent_pairFormation,
dependent_set_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality
Latex:
\mforall{}[X:SeparationSpace]. \mforall{}[p:Point(Path(X))]. \mforall{}[t:\{t:\mBbbR{}| t \mmember{} [r0, r1]\} ]. (p@t \mmember{} Point(X))
Date html generated:
2020_05_20-PM-01_20_15
Last ObjectModification:
2018_06_29-PM-05_47_40
Theory : intuitionistic!topology
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