Nuprl Lemma : geo-construction-unicity-from-first
∀e:BasicGeometry-. ∀[Q,A,X,Y:Point]. (X ≡ Y) supposing (QY ≅ QX and Q_A_X and Q_A_Y and Q ≠ A)
Proof
Definitions occuring in Statement :
basic-geometry-: BasicGeometry-,
geo-eq: a ≡ b,
geo-congruent: ab ≅ cd,
geo-between: a_b_c,
geo-sep: a ≠ b,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
geo-eq: a ≡ b,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
basic-geometry-: BasicGeometry-,
and: P ∧ Q
Lemmas referenced :
geo-congruent_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
basic-geometry--subtype,
subtype_rel_transitivity,
basic-geometry-_wf,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-between_wf,
geo-sep_wf,
geo-point_wf,
geo-congruent-refl,
geo-five-segment,
geo-congruence-identity-sym,
geo-between-symmetry,
geo-inner-three-segment,
geo-congruent-full-symmetry
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality_alt,
dependent_functionElimination,
thin,
hypothesisEquality,
because_Cache,
functionIsTypeImplies,
inhabitedIsType,
universeIsType,
extract_by_obid,
isectElimination,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
isect_memberEquality_alt,
isectIsTypeImplies,
voidElimination,
productElimination
Latex:
\mforall{}e:BasicGeometry-. \mforall{}[Q,A,X,Y:Point]. (X \mequiv{} Y) supposing (QY \mcong{} QX and Q\_A\_X and Q\_A\_Y and Q \mneq{} A)
Date html generated:
2019_10_16-PM-01_16_11
Last ObjectModification:
2019_01_03-PM-02_02_06
Theory : euclidean!plane!geometry
Home
Index