### Nuprl Lemma : eu-length-flip

`∀e:EuclideanPlane. ∀[a,b:Point].  (|ab| = |ba| ∈ {p:Point| O_X_p} )`

Proof

Definitions occuring in Statement :  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]` all: `∀x:A. B[x]` set: `{x:A| B[x]} ` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` eu-length: `|s|` euclidean-plane: `EuclideanPlane` and: `P ∧ Q` prop: `ℙ` uiff: `uiff(P;Q)` uimplies: `b supposing a` subtype_rel: `A ⊆r B`
Lemmas referenced :  eu-extend-property eu-O_wf eu-not-colinear-OXY eu-X_wf not_wf equal_wf eu-point_wf eu-seg1_wf eu-mk-seg_wf eu-seg2_wf eu-between-eq_wf eu-seg-congruent-iff-length eu-congruent-flip-seg
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation introduction cut dependent_set_memberEquality sqequalRule lemma_by_obid sqequalHypSubstitution dependent_functionElimination thin because_Cache isectElimination setElimination rename hypothesisEquality hypothesis productElimination isect_memberEquality axiomEquality independent_isectElimination applyEquality

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}[a,b:Point].    (|ab|  =  |ba|)

Date html generated: 2016_05_18-AM-06_37_41
Last ObjectModification: 2015_12_28-AM-09_24_39

Theory : euclidean!geometry

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