### Nuprl Lemma : eu-extend-exists

`∀e:EuclideanPlane. ∀q:Point. ∀a:{a:Point| ¬(q = a ∈ Point)} . ∀b,c:Point.  ∃x:Point. (q_a_x ∧ ax=bc)`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-congruent: `ab=cd` eu-point: `Point` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` not: `¬A` and: `P ∧ Q` set: `{x:A| B[x]} ` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` exists: `∃x:A. B[x]` member: `t ∈ T` uall: `∀[x:A]. B[x]` euclidean-plane: `EuclideanPlane` and: `P ∧ Q` cand: `A c∧ B` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  eu-extend_wf eu-extend-property and_wf eu-between-eq_wf eu-congruent_wf eu-point_wf set_wf not_wf equal_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation dependent_pairFormation cut lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis dependent_functionElimination because_Cache productElimination independent_pairFormation sqequalRule lambdaEquality

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}q:Point.  \mforall{}a:\{a:Point|  \mneg{}(q  =  a)\}  .  \mforall{}b,c:Point.    \mexists{}x:Point.  (q\_a\_x  \mwedge{}  ax=bc)

Date html generated: 2016_05_18-AM-06_33_45
Last ObjectModification: 2015_12_28-AM-09_28_01

Theory : euclidean!geometry

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