### Nuprl Lemma : eu-seg-congruent_symmetry

`∀e:EuclideanPlane. ∀[s1,s2:Segment].  s2 ≡ s1 supposing s1 ≡ s2`

Proof

Definitions occuring in Statement :  eu-seg-congruent: `s1 ≡ s2` eu-segment: `Segment` euclidean-plane: `EuclideanPlane` uimplies: `b 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: `b supposing a` eu-seg-congruent: `s1 ≡ s2` member: `t ∈ T` euclidean-plane: `EuclideanPlane` prop: `ℙ`
Lemmas referenced :  eu-congruent-symmetry eu-seg1_wf eu-seg2_wf eu-seg-congruent_wf eu-segment_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation sqequalHypSubstitution cut lemma_by_obid dependent_functionElimination thin hypothesisEquality isectElimination setElimination rename hypothesis independent_isectElimination

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}[s1,s2:Segment].    s2  \mequiv{}  s1  supposing  s1  \mequiv{}  s2

Date html generated: 2016_05_18-AM-06_36_48
Last ObjectModification: 2015_12_28-AM-09_25_31

Theory : euclidean!geometry

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