Nuprl Lemma : dist_wf
∀[g:EuclideanPlaneStructure]. ∀[a,b,c,d,e,f:Point]. (D(a;b;c;d;e;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
dist: D(a;b;c;d;e;f),
euclidean-plane-structure: EuclideanPlaneStructure,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dist: D(a;b;c;d;e;f),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
exists_wf,
geo-point_wf,
geo-sep_wf,
geo-between_wf,
geo-congruent_wf,
euclidean-plane-structure-subtype,
euclidean-plane-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
lambdaEquality,
setEquality,
productEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[g:EuclideanPlaneStructure]. \mforall{}[a,b,c,d,e,f:Point]. (D(a;b;c;d;e;f) \mmember{} \mBbbP{})
Date html generated:
2019_10_16-PM-02_44_12
Last ObjectModification:
2018_09_21-AM-09_25_34
Theory : euclidean!plane!geometry
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