Nuprl Lemma : geo-lt-angle-symm2
∀g:EuclideanPlane. ∀a,b,c,d,e,f:Point. (abc < def ⇒ cba < def)
Proof
Definitions occuring in Statement :
geo-lt-angle: abc < xyz,
euclidean-plane: EuclideanPlane,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
geo-lt-angle: abc < xyz,
and: P ∧ Q,
exists: ∃x:A. B[x],
basic-geometry: BasicGeometry,
cand: A c∧ B,
geo-cong-angle: abc ≅a xyz
Lemmas referenced :
geo-lt-angle_wf,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-cong-angle-preserves-lt-angle,
geo-cong-angle-symm,
euclidean-plane-axioms
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
inhabitedIsType,
isectElimination,
applyEquality,
instantiate,
independent_isectElimination,
sqequalRule,
independent_functionElimination,
productElimination,
independent_pairFormation,
because_Cache
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c,d,e,f:Point. (abc < def {}\mRightarrow{} cba < def)
Date html generated:
2019_10_16-PM-02_01_38
Last ObjectModification:
2019_09_12-AM-11_37_45
Theory : euclidean!plane!geometry
Home
Index