Nuprl Lemma : geo-gt-irrefl
∀e:EuclideanPlane. ∀a,b:Point. (¬ab > ab)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-gt: cd > ab,
geo-point: Point,
all: ∀x:A. B[x],
not: ¬A
Definitions unfolded in proof :
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
geo-gt: cd > ab,
squash: ↓T,
exists: ∃x:A. B[x],
and: 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,
euclidean-plane: EuclideanPlane,
basic-geometry-: BasicGeometry-,
uiff: uiff(P;Q),
geo-eq: a ≡ b
Lemmas referenced :
geo-gt_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-point_wf,
geo-between-symmetry,
geo-between-sep,
geo-sep-sym,
geo-proper-extend-exists,
geo-O_wf,
geo-X_wf,
geo-sep-O-X,
geo-construction-unicity,
geo-strict-between-sep3,
geo-strict-between-implies-between,
geo-between-exchange3,
geo-between-exchange4,
geo-congruent-iff-length
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
thin,
sqequalHypSubstitution,
imageElimination,
productElimination,
hypothesis,
because_Cache,
independent_functionElimination,
voidElimination,
universeIsType,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
applyEquality,
instantiate,
independent_isectElimination,
sqequalRule,
inhabitedIsType,
dependent_functionElimination,
setElimination,
rename,
equalitySymmetry
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b:Point. (\mneg{}ab > ab)
Date html generated:
2019_10_16-PM-01_16_45
Last ObjectModification:
2019_04_19-PM-02_44_54
Theory : euclidean!plane!geometry
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