Nuprl Lemma : euclidean-point-eq
∀[e:EuclideanPlane]. ∀[p,q:Point]. p = q ∈ Point supposing ¬¬(p = q ∈ Point)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
stable: Stable{P},
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
euclidean-plane: EuclideanPlane
Lemmas referenced :
stable_point-eq,
not_wf,
equal_wf,
eu-point_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
lambdaFormation,
independent_functionElimination,
voidElimination,
setElimination,
rename,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[p,q:Point]. p = q supposing \mneg{}\mneg{}(p = q)
Date html generated:
2016_05_18-AM-06_34_05
Last ObjectModification:
2015_12_28-AM-09_27_29
Theory : euclidean!geometry
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