`∀[e:EuclideanPlane]. ∀[x:{p:Point| O_X_p} ]. ∀[a:Point].  (x + |aa| = x ∈ {p:Point| O_X_p} )`

Proof

Definitions occuring in Statement :  eu-add-length: `p + q` eu-length: `|s|` eu-mk-seg: `ab` euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-X: `X` eu-O: `O` eu-point: `Point` uall: `∀[x:A]. B[x]` set: `{x:A| B[x]} ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` euclidean-plane: `EuclideanPlane` all: `∀x:A. B[x]` prop: `ℙ` squash: `↓T` true: `True` uimplies: `b supposing a` guard: `{T}` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` implies: `P `` Q`
Lemmas referenced :  iff_weakening_equal eu-length-null-segment euclidean-plane_wf true_wf squash_wf eu-add-length_wf eu-X_wf eu-O_wf eu-between-eq_wf eu-point_wf eu-add-length-zero
Rules used in proof :  cut lemma_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation hypothesis sqequalHypSubstitution isectElimination thin hypothesisEquality equalityEquality setEquality setElimination rename dependent_functionElimination applyEquality lambdaEquality imageElimination equalityTransitivity equalitySymmetry because_Cache natural_numberEquality sqequalRule imageMemberEquality baseClosed independent_isectElimination productElimination independent_functionElimination

Latex:
\mforall{}[e:EuclideanPlane].  \mforall{}[x:\{p:Point|  O\_X\_p\}  ].  \mforall{}[a:Point].    (x  +  |aa|  =  x)

Date html generated: 2016_05_18-AM-06_38_17
Last ObjectModification: 2016_01_16-PM-10_29_51

Theory : euclidean!geometry

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