`∀[e:EuclideanPlane]. ∀[x,y:{p:Point| O_X_p} ].  (x + y ∈ {p:Point| O_X_p} )`

Proof

Definitions occuring in Statement :  eu-add-length: `p + q` euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-X: `X` eu-O: `O` eu-point: `Point` uall: `∀[x:A]. B[x]` member: `t ∈ T` set: `{x:A| B[x]} `
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` euclidean-plane: `EuclideanPlane` and: `P ∧ Q` not: `¬A` implies: `P `` Q` all: `∀x:A. B[x]` uimplies: `b supposing a` false: `False` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` eu-add-length: `p + q`
Lemmas referenced :  eu-not-colinear-OXY eu-between-eq-same2 eu-X_wf equal_wf eu-point_wf eu-O_wf set_wf eu-between-eq_wf euclidean-plane_wf eu-extend_wf not_wf eu-extend-property eu-between-eq-symmetry eu-between-eq-inner-trans eu-between-eq-exchange3 eu-between-eq-exchange4 and_wf eu-congruent_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality productElimination hypothesis lambdaFormation equalityTransitivity equalitySymmetry dependent_functionElimination independent_isectElimination independent_functionElimination voidElimination sqequalRule axiomEquality lambdaEquality isect_memberEquality because_Cache dependent_set_memberEquality equalityEquality

Latex:
\mforall{}[e:EuclideanPlane].  \mforall{}[x,y:\{p:Point|  O\_X\_p\}  ].    (x  +  y  \mmember{}  \{p:Point|  O\_X\_p\}  )

Date html generated: 2016_05_18-AM-06_37_51
Last ObjectModification: 2015_12_28-AM-09_25_03

Theory : euclidean!geometry

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