Nuprl Lemma : sq_stable-pgeo-axioms-if
∀[g:ProjGeomPrimitives]. ((∀a:Point. ∀L:Line. SqStable(a ≠ L)) ⇒ SqStable(BasicProjectiveGeometryAxioms(g)))
Proof
Definitions occuring in Statement :
basic-pgeo-axioms: BasicProjectiveGeometryAxioms(g),
pgeo-plsep: a ≠ b,
pgeo-primitives: ProjGeomPrimitives,
pgeo-line: Line,
pgeo-point: Point,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
basic-pgeo-axioms: BasicProjectiveGeometryAxioms(g),
pgeo-leq: a ≡ b,
pgeo-peq: a ≡ b,
pgeo-incident: a I b,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
and: P ∧ Q,
all: ∀x:A. B[x],
sq_stable: SqStable(P),
not: ¬A,
false: False
Lemmas referenced :
sq_stable__and,
all_wf,
pgeo-point_wf,
not_wf,
pgeo-psep_wf,
pgeo-line_wf,
pgeo-lsep_wf,
pgeo-plsep_wf,
sq_stable__all,
sq_stable__not,
sq_stable_wf,
pgeo-peq_wf,
pgeo-leq_wf,
pgeo-incident_wf,
squash_wf,
basic-pgeo-axioms_wf,
pgeo-primitives_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
isect_memberEquality,
productEquality,
because_Cache,
functionEquality,
independent_functionElimination,
dependent_functionElimination,
productElimination,
independent_pairEquality,
voidElimination
Latex:
\mforall{}[g:ProjGeomPrimitives]
((\mforall{}a:Point. \mforall{}L:Line. SqStable(a \mneq{} L)) {}\mRightarrow{} SqStable(BasicProjectiveGeometryAxioms(g)))
Date html generated:
2018_05_22-PM-00_26_24
Last ObjectModification:
2017_10_30-PM-01_38_05
Theory : euclidean!plane!geometry
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