Nuprl Lemma : geo-O_wf
∀e:EuclideanPlaneStructure. (O ∈ Point)
Proof
Definitions occuring in Statement :
geo-O: O,
euclidean-plane-structure: EuclideanPlaneStructure,
geo-point: Point,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
top: Top,
implies: P ⇒ Q,
prop: ℙ,
exists: ∃x:A. B[x],
sq_exists: ∃x:{A| B[x]},
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
geo-O: O,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
euclidean-plane-structure_wf,
equal_wf,
pi1_wf_top,
geo-sep_wf,
sq_exists_wf,
euclidean-plane-structure-subtype,
geo-point_wf,
exists_wf,
geo-nontrivial_wf
Rules used in proof :
independent_functionElimination,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
voidEquality,
voidElimination,
isect_memberEquality,
independent_pairEquality,
productElimination,
because_Cache,
lambdaEquality,
sqequalRule,
applyEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:EuclideanPlaneStructure. (O \mmember{} Point)
Date html generated:
2017_10_02-PM-03_28_24
Last ObjectModification:
2017_08_04-PM-08_49_47
Theory : euclidean!plane!geometry
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