Nuprl Lemma : angle-sum_wf
∀e:EuclideanPlane. ∀a,b,c,x,y,z,i,j,k:Point. (abc + xyz ≅a ijk ∈ ℙ)
Proof
Definitions occuring in Statement :
angle-sum: abc + def ≅a xyz,
euclidean-plane: EuclideanPlane,
geo-point: Point,
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
angle-sum: abc + def ≅a xyz,
prop: ℙ,
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
basic-geometry: BasicGeometry,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
geo-point_wf,
geo-left_wf,
geo-cong-angle_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,
lambdaFormation_alt,
cut,
sqequalRule,
productEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
inhabitedIsType,
universeIsType,
instantiate,
independent_isectElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,x,y,z,i,j,k:Point. (abc + xyz \mcong{}\msuba{} ijk \mmember{} \mBbbP{})
Date html generated:
2019_10_16-PM-02_03_23
Last ObjectModification:
2019_06_10-PM-07_46_18
Theory : euclidean!plane!geometry
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