Nuprl Lemma : pgeo-non-trivial-dual
∀g:ProjectivePlane. (∃l:Line [l ≡ l])
Proof
Definitions occuring in Statement : 
projective-plane: ProjectivePlane
, 
pgeo-leq: a ≡ b
, 
pgeo-line: Line
, 
all: ∀x:A. B[x]
, 
sq_exists: ∃x:A [B[x]]
Definitions unfolded in proof : 
prop: ℙ
, 
implies: P 
⇒ Q
, 
sq_exists: ∃x:A [B[x]]
, 
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-primitives_wf, 
projective-plane-structure_subtype, 
pgeo-leq_wf, 
pgeo-leq_weakening, 
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-lines-axiom, 
pgeo-non-trivial
Rules used in proof : 
independent_functionElimination, 
because_Cache, 
dependent_set_memberEquality, 
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{}l:Line  [l  \mequiv{}  l])
Date html generated:
2018_05_22-PM-00_47_39
Last ObjectModification:
2017_11_27-PM-04_31_35
Theory : euclidean!plane!geometry
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