Nuprl Lemma : dist-cong_wf
∀[g1:EuclideanPlane]. ∀[a,b,c,d:Point]. (Dcong(g1;a;b;c;d) ∈ ℙ)
Proof
Definitions occuring in Statement :
dist-cong: Dcong(g;a;b;c;d),
euclidean-plane: EuclideanPlane,
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-cong: Dcong(g;a;b;c;d),
prop: ℙ,
and: P ∧ Q,
euclidean-plane: EuclideanPlane,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
not_wf,
dist_wf,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
universeIsType,
applyEquality,
instantiate,
independent_isectElimination
Latex:
\mforall{}[g1:EuclideanPlane]. \mforall{}[a,b,c,d:Point]. (Dcong(g1;a;b;c;d) \mmember{} \mBbbP{})
Date html generated:
2019_10_16-PM-02_47_13
Last ObjectModification:
2018_10_02-AM-11_12_39
Theory : euclidean!plane!geometry
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