Nuprl Lemma : pgeo-plsep-to-psep2
∀g:ProjectivePlane. ∀a:Point. ∀l:Line. (a ≠ l ⇒ (∀b:{b:Point| b I l} . a ≠ b))
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-psep: a ≠ b,
pgeo-incident: a I b,
pgeo-plsep: a ≠ b,
pgeo-line: Line,
pgeo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]}
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
squash: ↓T,
sq_stable: SqStable(P),
uimplies: b supposing a,
guard: {T},
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-line_wf,
pgeo-plsep_wf,
pgeo-incident_wf,
pgeo-primitives_wf,
projective-plane-structure_subtype,
pgeo-point_wf,
set_wf,
pgeo-psep-sym,
sq_stable__pgeo-incident,
projective-plane-structure_wf,
projective-plane-structure-complete_wf,
projective-plane_wf,
subtype_rel_transitivity,
projective-plane-subtype,
projective-plane-structure-complete_subtype,
pgeo-plsep-to-psep
Rules used in proof :
lambdaEquality,
imageElimination,
baseClosed,
imageMemberEquality,
because_Cache,
independent_functionElimination,
rename,
setElimination,
sqequalRule,
independent_isectElimination,
isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane. \mforall{}a:Point. \mforall{}l:Line. (a \mneq{} l {}\mRightarrow{} (\mforall{}b:\{b:Point| b I l\} . a \mneq{} b))
Date html generated:
2018_05_22-PM-00_48_32
Last ObjectModification:
2018_01_05-PM-08_32_31
Theory : euclidean!plane!geometry
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