### Nuprl Lemma : eu-congruent-trivial

`∀e:EuclideanPlane. ∀[a,b:Point].  aa=bb`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-congruent: `ab=cd` eu-point: `Point` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` euclidean-plane: `EuclideanPlane` stable: `Stable{P}` uimplies: `b supposing a` not: `¬A` implies: `P `` Q` prop: `ℙ` false: `False` and: `P ∧ Q` exists: `∃x:A. B[x]`
Lemmas referenced :  stable__eu-congruent not_wf eu-congruent_wf eu-point_wf euclidean-plane_wf eu-congruent-refl equal_wf eu-extend-exists eu-congruence-identity and_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination thin setElimination rename hypothesisEquality hypothesis isectElimination because_Cache independent_isectElimination independent_functionElimination hyp_replacement equalitySymmetry Error :applyLambdaEquality,  sqequalRule voidElimination dependent_set_memberEquality productElimination independent_pairFormation applyEquality lambdaEquality setEquality

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}[a,b:Point].    aa=bb

Date html generated: 2016_10_26-AM-07_41_03
Last ObjectModification: 2016_07_12-AM-08_07_17

Theory : euclidean!geometry

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