`∀[e:EuclideanPlane]. ∀[x:{p:Point| O_X_p} ].  (x + X = x ∈ {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]` 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` so_lambda: `λ2x.t[x]` so_apply: `x[s]` eu-add-length: `p + q` and: `P ∧ Q` not: `¬A` implies: `P `` Q` uimplies: `b supposing a` false: `False` sq_stable: `SqStable(P)` squash: `↓T`
Lemmas referenced :  eu-between-eq_wf eu-O_wf eu-X_wf set_wf eu-point_wf euclidean-plane_wf eu-not-colinear-OXY eu-between-eq-same equal_wf not_wf eu-extend_wf eu-congruence-identity eu-congruent_wf eu-extend-property eu-add-length_wf eu-between-eq-trivial-right sq_stable__eu-between-eq
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut dependent_set_memberEquality extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis dependent_functionElimination because_Cache sqequalRule lambdaEquality isect_memberEquality axiomEquality productElimination lambdaFormation equalitySymmetry hyp_replacement Error :applyLambdaEquality,  equalityTransitivity independent_isectElimination independent_functionElimination voidElimination productEquality equalityEquality imageMemberEquality baseClosed imageElimination

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

Date html generated: 2016_10_26-AM-07_41_58
Last ObjectModification: 2016_07_12-AM-08_08_10

Theory : euclidean!geometry

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