### Nuprl Lemma : eu-add-length-cancel-right

`∀[e:EuclideanPlane]. ∀[x,y,z:{p:Point| O_X_p} ].  x = y ∈ {p:Point| O_X_p}  supposing x + z = 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` uimplies: `b supposing a` 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` uimplies: `b supposing a` prop: `ℙ` euclidean-plane: `EuclideanPlane` all: `∀x:A. B[x]` guard: `{T}` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` implies: `P `` Q`
Lemmas referenced :  eu-add-length-cancel-left equal_wf eu-point_wf eu-between-eq_wf eu-O_wf eu-X_wf eu-add-length_wf euclidean-plane_wf eu-add-length-comm iff_weakening_equal
Rules used in proof :  cut lemma_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation hypothesis sqequalHypSubstitution isectElimination thin hypothesisEquality independent_isectElimination setEquality setElimination rename dependent_functionElimination equalityEquality equalityTransitivity equalitySymmetry productElimination independent_functionElimination

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

Date html generated: 2016_05_18-AM-06_38_34
Last ObjectModification: 2015_12_28-AM-09_24_23

Theory : euclidean!geometry

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