### Nuprl Lemma : eu-congruent-left-comm

e:EuclideanPlane. ∀[a,b,c,d:Point].  ba=cd supposing ab=cd

Proof

Definitions occuring in Statement :  euclidean-plane: EuclideanPlane eu-congruent: ab=cd eu-point: Point uimplies: supposing a uall: [x:A]. B[x] all: x:A. B[x]
Definitions unfolded in proof :  all: x:A. B[x] uall: [x:A]. B[x] uimplies: supposing a member: t ∈ T prop: euclidean-plane: EuclideanPlane sq_stable: SqStable(P) implies:  Q euclidean-axioms: euclidean-axioms(e) and: P ∧ Q squash: T guard: {T}
Lemmas referenced :  eu-congruent-refl sq_stable__eu-congruent euclidean-plane_wf eu-point_wf eu-congruent_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut hypothesisEquality lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesis dependent_functionElimination independent_functionElimination introduction productElimination sqequalRule imageMemberEquality baseClosed imageElimination equalityTransitivity equalitySymmetry because_Cache independent_isectElimination

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}[a,b,c,d:Point].    ba=cd  supposing  ab=cd

Date html generated: 2016_05_18-AM-06_34_57
Last ObjectModification: 2016_01_16-PM-10_31_14

Theory : euclidean!geometry

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