Nuprl Lemma : symmetric-point-unicity
∀e:BasicGeometry. ∀a,p,p1,p2:Point. (p=a=p1 ⇒ p=a=p2 ⇒ p1 ≡ p2)
Proof
Definitions occuring in Statement :
geo-midpoint: a=m=b,
basic-geometry: BasicGeometry,
geo-eq: a ≡ b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
and: P ∧ Q,
geo-midpoint: a=m=b,
iff: P ⇐⇒ Q,
false: False,
or: P ∨ Q,
not: ¬A,
stable: Stable{P},
geo-eq: a ≡ b,
uiff: uiff(P;Q)
Lemmas referenced :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
geo-midpoint_wf,
minimal-not-not-excluded-middle,
geo-eq_inversion,
geo-between-same,
geo-congruence-identity,
geo-between_functionality,
geo-eq_weakening,
geo-congruent_functionality,
minimal-double-negation-hyp-elim,
not_wf,
or_wf,
false_wf,
geo-sep_wf,
stable__not,
geo-congruent-iff-length,
geo-construction-unicity
Rules used in proof :
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
productElimination,
promote_hyp,
dependent_functionElimination,
voidElimination,
unionElimination,
independent_functionElimination,
functionEquality,
equalitySymmetry,
equalityTransitivity
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,p,p1,p2:Point. (p=a=p1 {}\mRightarrow{} p=a=p2 {}\mRightarrow{} p1 \mequiv{} p2)
Date html generated:
2017_10_02-PM-06_32_18
Last ObjectModification:
2017_08_05-PM-04_43_06
Theory : euclidean!plane!geometry
Home
Index