Nuprl Lemma : pgeo-sep-points-exist
∀g:ProjectivePlane. ∃a,b:Point. a ≠ b
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-psep: a ≠ b,
pgeo-point: Point,
all: ∀x:A. B[x],
exists: ∃x:A. B[x]
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
uimplies: b supposing a,
guard: {T},
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
exists: ∃x:A. B[x],
projective-plane: ProjectivePlane,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-point_wf,
exists_wf,
pgeo-primitives_wf,
projective-plane-structure_subtype,
pgeo-psep_wf,
projective-plane-structure_wf,
projective-plane-structure-complete_wf,
projective-plane_wf,
subtype_rel_transitivity,
projective-plane-subtype,
projective-plane-structure-complete_subtype,
pgeo-three-points-axiom,
point-implies-plsep-exists,
pgeo-non-trivial
Rules used in proof :
lambdaEquality,
because_Cache,
dependent_pairFormation,
sqequalRule,
independent_isectElimination,
isectElimination,
instantiate,
applyEquality,
productElimination,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane. \mexists{}a,b:Point. a \mneq{} b
Date html generated:
2018_05_22-PM-00_52_39
Last ObjectModification:
2017_11_28-PM-04_58_26
Theory : euclidean!plane!geometry
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