Nuprl Lemma : ss-free-homotopic_weakening
∀X:SeparationSpace. ∀a,b:Point(X). ss-free-homotopic(X;a;b) supposing a ≡ b
Proof
Definitions occuring in Statement :
ss-free-homotopic: ss-free-homotopic(X;a;b),
ss-eq: x ≡ y,
ss-point: Point(ss),
separation-space: SeparationSpace,
uimplies: b supposing a,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
ss-eq: x ≡ y,
not: ¬A,
implies: P ⇒ Q,
false: False,
ss-free-homotopic: ss-free-homotopic(X;a;b),
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
path-at: p@t,
guard: {T},
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
le: A ≤ B,
less_than': less_than'(a;b),
prop: ℙ
Lemmas referenced :
ss-eq_inversion,
ss-eq_functionality,
ss-eq_weakening,
ss-eq_wf,
path-at_wf,
member_rccint_lemma,
rleq_weakening_equal,
int-to-real_wf,
rleq-int,
istype-false,
rleq_wf,
ss-point_wf,
separation-space_wf,
path-ss-point,
real_wf,
unit-ss_wf,
unit_ss_point_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
isect_memberFormation_alt,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality_alt,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
functionIsTypeImplies,
inhabitedIsType,
rename,
dependent_pairFormation_alt,
extract_by_obid,
independent_functionElimination,
hypothesis,
independent_pairFormation,
because_Cache,
independent_isectElimination,
productElimination,
productIsType,
universeIsType,
isectElimination,
Error :memTop,
natural_numberEquality,
dependent_set_memberEquality_alt,
setIsType,
functionIsType,
applyEquality
Latex:
\mforall{}X:SeparationSpace. \mforall{}a,b:Point(X). ss-free-homotopic(X;a;b) supposing a \mequiv{} b
Date html generated:
2020_05_20-PM-01_20_26
Last ObjectModification:
2020_02_08-AM-11_41_37
Theory : intuitionistic!topology
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