Nuprl Lemma : segment-density
∀e:EuclideanPlane. ∀a,b:Point. ∃x:Point. a_x_b
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-between: a_b_c,
geo-point: Point,
all: ∀x:A. B[x],
exists: ∃x:A. B[x]
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
uall: ∀[x:A]. B[x],
basic-geometry-: BasicGeometry-,
member: t ∈ T,
exists: ∃x:A. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
geo-point_wf,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-between_wf,
geo-between-trivial
Rules used in proof :
because_Cache,
independent_isectElimination,
instantiate,
applyEquality,
hypothesis,
isectElimination,
sqequalRule,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
hypothesisEquality,
dependent_pairFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b:Point. \mexists{}x:Point. a\_x\_b
Date html generated:
2017_10_02-PM-06_55_02
Last ObjectModification:
2017_08_06-PM-07_54_57
Theory : euclidean!plane!geometry
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