Nuprl Lemma : eu-X_wf
∀e:EuclideanStructure. (X ∈ Point)
Proof
Definitions occuring in Statement :
eu-X: X,
eu-point: Point,
euclidean-structure: EuclideanStructure,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
eu-X: X,
uall: ∀[x:A]. B[x],
spreadn: spread3,
and: P ∧ Q,
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top
Lemmas referenced :
eu-nontrivial_wf,
eu-point_wf,
not_wf,
equal_wf,
eu-colinear_wf,
pi1_wf_top,
pi2_wf,
subtype_rel_product,
top_wf,
euclidean-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setEquality,
productEquality,
because_Cache,
productElimination,
sqequalRule,
lambdaEquality,
setElimination,
rename,
applyEquality,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
equalityEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}e:EuclideanStructure. (X \mmember{} Point)
Date html generated:
2016_05_18-AM-06_32_38
Last ObjectModification:
2015_12_28-AM-09_28_13
Theory : euclidean!geometry
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