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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