Nuprl Lemma : geo-lt-angle-symm
∀g:EuclideanPlane. ∀a,b,c,d,e,f:Point. (abc < def ⇒ d # ef ⇒ abc < fed)
Proof
Definitions occuring in Statement :
geo-lt-angle: abc < xyz,
euclidean-plane: EuclideanPlane,
geo-lsep: a # bc,
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,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
basic-geometry: BasicGeometry,
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
geo-lsep_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-lt-angle_wf,
geo-point_wf,
geo-cong-angle-symm,
euclidean-plane-axioms,
lsep-implies-sep,
geo-sep-sym,
lsep-symmetry,
geo-cong-angle-preserves-lt-angle2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
sqequalRule,
dependent_functionElimination,
inhabitedIsType,
because_Cache,
independent_functionElimination,
productElimination,
independent_pairFormation
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c,d,e,f:Point. (abc < def {}\mRightarrow{} d \# ef {}\mRightarrow{} abc < fed)
Date html generated:
2019_10_16-PM-02_01_25
Last ObjectModification:
2018_11_28-AM-11_43_17
Theory : euclidean!plane!geometry
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