Nuprl Lemma : path-at_functionality2
∀[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),
unit-ss: 𝕀,
ss-eq: x ≡ y,
ss-point: Point(ss),
separation-space: SeparationSpace,
rccint: [l, u],
i-member: r ∈ I,
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,
ss-eq: x ≡ y,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
all: ∀x:A. B[x],
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
ss-sep_wf,
path-at_wf,
ss-eq_wf,
unit-ss_wf,
member_rccint_lemma,
unit_ss_point_lemma,
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,
ss-eq_weakening,
ss-eq_functionality,
path-at_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
because_Cache,
extract_by_obid,
isectElimination,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
productElimination,
independent_pairFormation,
independent_isectElimination,
independent_functionElimination
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 \mequiv{} t\000C'
Date html generated:
2020_05_20-PM-01_20_19
Last ObjectModification:
2018_07_03-PM-05_15_54
Theory : intuitionistic!topology
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