`∀[e:EuclideanPlane]. ∀[x,y,z:{p:Point| O_X_p} ].  (x + y + z = x + y + z ∈ {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` cand: `A c∧ B` uiff: `uiff(P;Q)` squash: `↓T` true: `True` sq_stable: `SqStable(P)`
Lemmas referenced :  sq_stable__eu-between-eq eu-between-eq-exchange4 eu-construction-unicity eu-between-eq-exchange3 eu-between-eq-inner-trans eu-between-eq-symmetry eu-add-length-between euclidean-plane_wf true_wf squash_wf eu-add-length_wf eu-congruent-iff-length eu-congruent_wf and_wf eu-extend_wf not_wf eu-extend-property equal_wf eu-between-eq-same2 eu-not-colinear-OXY eu-point_wf set_wf eu-X_wf eu-O_wf eu-between-eq_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut dependent_set_memberEquality lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality dependent_functionElimination hypothesis sqequalRule lambdaEquality isect_memberEquality axiomEquality because_Cache productElimination lambdaFormation equalityTransitivity equalitySymmetry independent_isectElimination independent_functionElimination voidElimination equalityEquality applyEquality imageElimination setEquality natural_numberEquality imageMemberEquality baseClosed independent_pairFormation

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

Date html generated: 2016_05_18-AM-06_38_28
Last ObjectModification: 2016_01_16-PM-10_29_49

Theory : euclidean!geometry

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