Nuprl Lemma : pgeo-peq_weakening
∀g:ProjectivePlane. ∀l,m:Point.  ((l = m ∈ Point) 
⇒ l ≡ m)
Proof
Definitions occuring in Statement : 
projective-plane: ProjectivePlane
, 
pgeo-peq: a ≡ b
, 
pgeo-point: Point
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uimplies: b supposing a
, 
guard: {T}
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
false: False
, 
pgeo-incident: a I b
, 
and: P ∧ Q
, 
exists: ∃x:A. B[x]
, 
pgeo-psep: a ≠ b
, 
not: ¬A
, 
pgeo-peq: a ≡ b
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
Lemmas referenced : 
pgeo-primitives_wf, 
projective-plane-structure_wf, 
projective-plane-structure-complete_wf, 
projective-plane_wf, 
subtype_rel_transitivity, 
projective-plane-subtype, 
projective-plane-structure-complete_subtype, 
projective-plane-structure_subtype, 
pgeo-point_wf, 
equal_wf, 
pgeo-peq_wf, 
pgeo-psep_wf
Rules used in proof : 
independent_isectElimination, 
instantiate, 
applyLambdaEquality, 
equalitySymmetry, 
hyp_replacement, 
sqequalRule, 
because_Cache, 
applyEquality, 
hypothesisEquality, 
isectElimination, 
extract_by_obid, 
introduction, 
voidElimination, 
independent_functionElimination, 
productElimination, 
sqequalHypSubstitution, 
thin, 
hypothesis, 
cut, 
lambdaFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane.  \mforall{}l,m:Point.    ((l  =  m)  {}\mRightarrow{}  l  \mequiv{}  m)
Date html generated:
2018_05_22-PM-00_45_48
Last ObjectModification:
2017_11_27-PM-03_52_46
Theory : euclidean!plane!geometry
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