Nuprl Lemma : eu-congruence-identity3

`∀[e:EuclideanPlane]. ∀[a,b,c,d:Point].  (a = b ∈ Point) supposing (cd=ab and (c = d ∈ Point))`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-congruent: `ab=cd` eu-point: `Point` uimplies: `b supposing a` uall: `∀[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]`
Lemmas referenced :  eu-congruence-identity2 eu-congruent_wf equal_wf eu-point_wf euclidean-plane_wf eu-congruent-symmetry
Rules used in proof :  cut lemma_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation hypothesis sqequalHypSubstitution isectElimination thin hypothesisEquality introduction independent_isectElimination setElimination rename sqequalRule isect_memberEquality axiomEquality equalityTransitivity equalitySymmetry dependent_functionElimination

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

Date html generated: 2016_05_18-AM-06_35_12
Last ObjectModification: 2015_12_28-AM-09_26_11

Theory : euclidean!geometry

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