Nuprl Lemma : subtype-geo-length-type
∀[e:BasicGeometry]. ({p:Point| O_X_p} ⊆r Length)
Proof
Definitions occuring in Statement :
geo-length-type: Length,
basic-geometry: BasicGeometry,
geo-X: X,
geo-O: O,
geo-between: a_b_c,
geo-point: Point,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]}
Definitions unfolded in proof :
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
prop: ℙ,
basic-geometry: BasicGeometry,
all: ∀x:A. B[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
geo-length-type: Length
Lemmas referenced :
geo-length-equiv,
geo-eq_wf,
geo-X_wf,
geo-O_wf,
geo-between_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
subtype_quotient
Rules used in proof :
axiomEquality,
lambdaFormation,
lambdaEquality,
rename,
setElimination,
dependent_functionElimination,
because_Cache,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
setEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry]. (\{p:Point| O\_X\_p\} \msubseteq{}r Length)
Date html generated:
2017_10_02-PM-04_45_24
Last ObjectModification:
2017_08_05-AM-09_09_45
Theory : euclidean!plane!geometry
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