Nuprl Lemma : basic-pgeo-axioms_wf
∀[g:ProjGeomPrimitives]. (BasicProjectiveGeometryAxioms(g) ∈ ℙ)
Proof
Definitions occuring in Statement : 
basic-pgeo-axioms: BasicProjectiveGeometryAxioms(g)
, 
pgeo-primitives: ProjGeomPrimitives
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
basic-pgeo-axioms: BasicProjectiveGeometryAxioms(g)
, 
prop: ℙ
, 
and: P ∧ Q
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
Lemmas referenced : 
all_wf, 
pgeo-point_wf, 
not_wf, 
pgeo-psep_wf, 
pgeo-line_wf, 
pgeo-lsep_wf, 
pgeo-incident_wf, 
pgeo-peq_wf, 
pgeo-leq_wf, 
pgeo-primitives_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
productEquality, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
lambdaEquality, 
because_Cache, 
functionEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}[g:ProjGeomPrimitives].  (BasicProjectiveGeometryAxioms(g)  \mmember{}  \mBbbP{})
Date html generated:
2018_05_22-PM-00_26_15
Last ObjectModification:
2017_11_07-PM-00_02_36
Theory : euclidean!plane!geometry
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