### Nuprl Lemma : eu-lt_wf

`∀[e:EuclideanPlane]. ∀[p,q:{p:Point| O_X_p} ].  (p < q ∈ ℙ)`

Proof

Definitions occuring in Statement :  eu-lt: `p < q` euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-X: `X` eu-O: `O` eu-point: `Point` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` set: `{x:A| B[x]} `
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` eu-lt: `p < q` prop: `ℙ` and: `P ∧ Q` euclidean-plane: `EuclideanPlane` all: `∀x:A. B[x]` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  eu-le_wf eu-between-eq_wf eu-O_wf eu-X_wf not_wf equal_wf eu-point_wf set_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut setElimination thin rename sqequalRule productEquality lemma_by_obid sqequalHypSubstitution isectElimination hypothesisEquality dependent_set_memberEquality hypothesis dependent_functionElimination because_Cache axiomEquality equalityTransitivity equalitySymmetry lambdaEquality isect_memberEquality

Latex:
\mforall{}[e:EuclideanPlane].  \mforall{}[p,q:\{p:Point|  O\_X\_p\}  ].    (p  <  q  \mmember{}  \mBbbP{})

Date html generated: 2016_05_18-AM-06_37_29
Last ObjectModification: 2015_12_28-AM-09_25_11

Theory : euclidean!geometry

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