Nuprl Lemma : geo-eq-self
∀[e:EuclideanPlane]. ∀[a:Point]. a ≡ a
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-eq: a ≡ b,
geo-point: Point,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
geo-eq: a ≡ b,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
geo-sep_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-point_wf,
geo-eq_weakening
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,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
isect_memberEquality,
voidElimination
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[a:Point]. a \mequiv{} a
Date html generated:
2018_05_22-AM-11_53_09
Last ObjectModification:
2018_04_12-AM-10_06_31
Theory : euclidean!plane!geometry
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