Nuprl Lemma : pgeo-meet-incident
∀g:ProjectivePlaneStructure. ∀l,m:Line. ∀s:l ≠ m. (l ∧ m I l ∧ l ∧ m I m)
Proof
Definitions occuring in Statement :
pgeo-meet: l ∧ m,
projective-plane-structure: ProjectivePlaneStructure,
pgeo-lsep: l ≠ m,
pgeo-incident: a I b,
pgeo-line: Line,
all: ∀x:A. B[x],
and: P ∧ Q
Definitions unfolded in proof :
squash: ↓T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
cand: A c∧ B,
and: P ∧ Q,
all: ∀x:A. B[x]
Lemmas referenced :
projective-plane-structure_wf,
pgeo-line_wf,
pgeo-lsep_wf,
equal_wf,
projective-plane-structure_subtype,
sq_stable__pgeo-incident,
pgeo-incident_wf,
pgeo-point_wf,
set_wf,
pgeo-meet_wf
Rules used in proof :
independent_pairFormation,
equalitySymmetry,
equalityTransitivity,
imageElimination,
baseClosed,
imageMemberEquality,
independent_functionElimination,
productElimination,
rename,
setElimination,
productEquality,
lambdaEquality,
sqequalRule,
because_Cache,
applyEquality,
isectElimination,
hypothesis,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlaneStructure. \mforall{}l,m:Line. \mforall{}s:l \mneq{} m. (l \mwedge{} m I l \mwedge{} l \mwedge{} m I m)
Date html generated:
2018_05_22-PM-00_31_03
Last ObjectModification:
2017_11_16-PM-01_37_05
Theory : euclidean!plane!geometry
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