### Nuprl Lemma : eu-eqt

e:EuclideanPlane. ∀a,b,c:{p:Point| O_X_p} .
(((a b ∈ {p:Point| O_X_p} ) ∧ (b c ∈ {p:Point| O_X_p} ))  (a c ∈ {p:Point| O_X_p} ))

Proof

Definitions occuring in Statement :  euclidean-plane: EuclideanPlane eu-between-eq: a_b_c eu-X: X eu-O: O eu-point: Point all: x:A. B[x] implies:  Q and: P ∧ Q set: {x:A| B[x]}  equal: t ∈ T
Definitions unfolded in proof :  all: x:A. B[x] implies:  Q and: P ∧ Q member: t ∈ T prop: uall: [x:A]. B[x] euclidean-plane: EuclideanPlane so_lambda: λ2x.t[x] so_apply: x[s]
Lemmas referenced :  and_wf equal_wf eu-point_wf eu-between-eq_wf eu-O_wf eu-X_wf set_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut sqequalHypSubstitution productElimination thin equalityTransitivity hypothesis lemma_by_obid isectElimination setEquality setElimination rename hypothesisEquality dependent_functionElimination sqequalRule lambdaEquality

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}a,b,c:\{p:Point|  O\_X\_p\}  .    (((a  =  b)  \mwedge{}  (b  =  c))  {}\mRightarrow{}  (a  =  c))

Date html generated: 2016_05_18-AM-06_43_52
Last ObjectModification: 2015_12_28-AM-09_21_41

Theory : euclidean!geometry

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