### Nuprl Lemma : eu-seg-congruent_weakening

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

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]` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` uimplies: `b supposing a` member: `t ∈ T` eu-seg-congruent: `s1 ≡ s2` euclidean-plane: `EuclideanPlane` prop: `ℙ`
Lemmas referenced :  eu-congruent-refl eu-seg1_wf eu-seg2_wf eu-congruent_wf equal_wf eu-segment_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut introduction axiomEquality hypothesis thin rename extract_by_obid sqequalHypSubstitution dependent_functionElimination hypothesisEquality isectElimination setElimination because_Cache hyp_replacement equalitySymmetry Error :applyLambdaEquality,  sqequalRule

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

Date html generated: 2016_10_26-AM-07_41_28
Last ObjectModification: 2016_07_12-AM-08_07_34

Theory : euclidean!geometry

Home Index