Nuprl Lemma : geo-gt-sep
∀e:EuclideanPlane. ∀A,B,C,P:Point. (AB > CP ⇒ A ≠ B)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-gt: cd > ab,
geo-sep: a ≠ b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
geo-gt: cd > ab,
squash: ↓T,
member: t ∈ T,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
exists: ∃x:A. B[x],
and: P ∧ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ
Lemmas referenced :
sq_stable__geo-sep,
geo-between-sep,
geo-between-symmetry,
euclidean-plane-axioms,
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
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
independent_functionElimination,
productElimination,
isectElimination,
independent_isectElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
universeIsType,
applyEquality,
instantiate,
inhabitedIsType,
because_Cache
Latex:
\mforall{}e:EuclideanPlane. \mforall{}A,B,C,P:Point. (AB > CP {}\mRightarrow{} A \mneq{} B)
Date html generated:
2019_10_16-PM-01_14_08
Last ObjectModification:
2019_08_07-PM-02_51_43
Theory : euclidean!plane!geometry
Home
Index