Nuprl Lemma : geo-construction-unicity
∀e:BasicGeometry-. ∀[Q,A,X,Y:Point]. (X ≡ Y) supposing (AY ≅ AX 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 :
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
false: False,
implies: P ⇒ Q,
not: ¬A,
geo-eq: a ≡ b,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
geo-congruence-identity-sym,
geo-five-segment,
geo-congruent-refl,
geo-point_wf,
geo-between_wf,
geo-congruent_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry-_wf,
subtype_rel_transitivity,
basic-geometry--subtype,
geo-sep_wf,
geo-three-segment,
geo-congruent-symmetry
Rules used in proof :
voidElimination,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
isectElimination,
extract_by_obid,
because_Cache,
hypothesisEquality,
thin,
dependent_functionElimination,
lambdaEquality,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry-. \mforall{}[Q,A,X,Y:Point]. (X \mequiv{} Y) supposing (AY \00D0 AX and Q\_A\_X and Q\_A\_Y and Q \mneq{} A)
Date html generated:
2017_10_02-PM-04_51_05
Last ObjectModification:
2017_08_05-AM-08_42_08
Theory : euclidean!plane!geometry
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