### Nuprl Lemma : eu-between-eq-inner-trans

`∀e:EuclideanPlane. ∀[a,b,c,d:Point].  (a_b_c) supposing (b_c_d and a_b_d)`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-point: `Point` 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` member: `t ∈ T` euclidean-plane: `EuclideanPlane` sq_stable: `SqStable(P)` implies: `P `` Q` stable: `Stable{P}` not: `¬A` false: `False` prop: `ℙ` squash: `↓T` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` cand: `A c∧ B` true: `True` subtype_rel: `A ⊆r B` guard: `{T}`
Lemmas referenced :  sq_stable__eu-between-eq stable__eu-between-eq not_wf eu-between-eq_wf eu-point_wf euclidean-plane_wf eu-between-eq-def equal_wf eu-between_wf eu-between-trans stable__eu-between squash_wf true_wf euclidean-structure_wf iff_weakening_equal eu-between-same and_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination thin setElimination rename because_Cache hypothesis isectElimination hypothesisEquality independent_functionElimination independent_isectElimination addLevel voidElimination levelHypothesis sqequalRule imageMemberEquality baseClosed imageElimination productElimination productEquality independent_pairFormation equalitySymmetry equalityTransitivity applyEquality lambdaEquality universeEquality natural_numberEquality hyp_replacement dependent_set_memberEquality setEquality

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}[a,b,c,d:Point].    (a\_b\_c)  supposing  (b\_c\_d  and  a\_b\_d)

Date html generated: 2016_10_26-AM-07_40_59
Last ObjectModification: 2016_07_12-AM-08_07_10

Theory : euclidean!geometry

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