### Nuprl Lemma : eu-be-end-eq

`∀e:EuclideanPlane. ∀a,b,c:Point.  (a_b_c `` ab=ac `` (b = c ∈ Point))`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-congruent: `ab=cd` eu-point: `Point` all: `∀x:A. B[x]` implies: `P `` Q` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` prop: `ℙ` uall: `∀[x:A]. B[x]` euclidean-plane: `EuclideanPlane` uimplies: `b supposing a` uiff: `uiff(P;Q)` and: `P ∧ Q` squash: `↓T` true: `True` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` subtype_rel: `A ⊆r B`
Lemmas referenced :  eu-congruence-identity-sym eu-length-null-segment eu-between-eq-symmetry eu-between-eq-trivial-right eu-add-length-cancel-left eu-add-length-zero iff_weakening_equal eu-mk-seg_wf eu-length_wf true_wf squash_wf eu-add-length_wf eu-X_wf eu-O_wf eu-congruent-iff-length eu-add-length-between euclidean-plane_wf eu-point_wf eu-between-eq_wf eu-congruent_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut hypothesis lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality independent_isectElimination because_Cache dependent_functionElimination productElimination equalityEquality setEquality equalityTransitivity equalitySymmetry applyEquality lambdaEquality imageElimination natural_numberEquality sqequalRule imageMemberEquality baseClosed independent_functionElimination dependent_set_memberEquality universeEquality

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}a,b,c:Point.    (a\_b\_c  {}\mRightarrow{}  ab=ac  {}\mRightarrow{}  (b  =  c))

Date html generated: 2016_05_18-AM-06_45_35
Last ObjectModification: 2016_01_16-PM-10_29_28

Theory : euclidean!geometry

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