Nuprl Lemma : Euclid-Prop2
∀e:EuclideanPlane. ∀a,b,c:Point. (∃x:{Point| ax ≅ bc})
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-point: Point,
all: ∀x:A. B[x],
sq_exists: ∃x:{A| B[x]}
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
or: P ∨ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
euclidean-plane: EuclideanPlane,
exists: ∃x:A. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
sq_exists: ∃x:{A| B[x]}
Lemmas referenced :
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-point_wf,
geo-sep_wf,
geo-sep-or,
geo-sep-exists,
Euclid-Prop2-lemma-ext,
geo-congruent_wf,
geo-congruent-transitivity
Rules used in proof :
independent_isectElimination,
instantiate,
unionElimination,
sqequalRule,
applyEquality,
isectElimination,
dependent_set_memberEquality,
because_Cache,
hypothesis,
rename,
setElimination,
productElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c:Point. (\mexists{}x:\{Point| ax \00D0 bc\})
Date html generated:
2017_10_02-PM-04_49_47
Last ObjectModification:
2017_08_06-PM-02_51_00
Theory : euclidean!plane!geometry
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