Nuprl Lemma : rng-pp-primitives_wf
∀[r:Rng]. (rng-pp-primitives(r) ∈ ProjGeomPrimitives)
Proof
Definitions occuring in Statement :
rng-pp-primitives: rng-pp-primitives(r),
pgeo-primitives: ProjGeomPrimitives,
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng: Rng
Definitions unfolded in proof :
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
all: ∀x:A. B[x],
prop: ℙ,
rng: Rng,
rng-pp-primitives: rng-pp-primitives(r),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
rng_zero_wf,
le_wf,
false_wf,
scalar-product_wf,
zero-vector_wf,
equal_wf,
not_wf,
rng_car_wf,
int_seg_wf,
mk-pgeo-prim_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
independent_pairFormation,
dependent_set_memberEquality,
lambdaFormation,
lambdaEquality,
hypothesisEquality,
applyEquality,
functionExtensionality,
because_Cache,
rename,
setElimination,
hypothesis,
natural_numberEquality,
functionEquality,
setEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[r:Rng]. (rng-pp-primitives(r) \mmember{} ProjGeomPrimitives)
Date html generated:
2018_05_22-PM-00_53_12
Last ObjectModification:
2018_05_21-AM-01_20_06
Theory : euclidean!plane!geometry
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