Nuprl Lemma : test-prove-separated
∀e:BasicGeometry. ∀A,B,C,X,Y,Z,W,U,V:Point.
((A ≠ B ∨ A-X-B ∨ B-X-A) ⇒ (A_B_C ∨ C_B_A) ⇒ (Y_C_A ∨ A_C_Y) ⇒ (ZW ≅ AY ∨ ZW ≅ YA) ⇒ ZW ≅ UV ⇒ U ≠ V)
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-strict-between: a-b-c,
geo-congruent: ab ≅ cd,
geo-between: a_b_c,
geo-sep: a ≠ b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
or: P ∨ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
geo-point_wf,
geo-strict-between_wf,
geo-sep_wf,
geo-between_wf,
or_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-congruent_wf,
geo-strict-between-sep1,
geo-between-sep,
geo-between-symmetry,
geo-sep-sym,
geo-congruent-sep,
geo-congruent-symmetry
Rules used in proof :
sqequalRule,
instantiate,
applyEquality,
independent_functionElimination,
because_Cache,
hypothesis,
independent_isectElimination,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
extract_by_obid,
introduction,
cut,
thin,
unionElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}A,B,C,X,Y,Z,W,U,V:Point.
((A \mneq{} B \mvee{} A-X-B \mvee{} B-X-A)
{}\mRightarrow{} (A\_B\_C \mvee{} C\_B\_A)
{}\mRightarrow{} (Y\_C\_A \mvee{} A\_C\_Y)
{}\mRightarrow{} (ZW \00D0 AY \mvee{} ZW \00D0 YA)
{}\mRightarrow{} ZW \00D0 UV
{}\mRightarrow{} U \mneq{} V)
Date html generated:
2017_10_02-PM-06_20_26
Last ObjectModification:
2017_08_05-PM-04_14_59
Theory : euclidean!plane!geometry
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