Nuprl Lemma : geo-colinear-same-side2
∀e:BasicGeometry. ∀[A,B,C,D:Point]. (Colinear(A;C;D)) supposing (A ≠ B and A_B_C and A_B_D)
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-colinear: Colinear(a;b;c),
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 :
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
cand: A c∧ B,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
geo-colinear: Colinear(a;b;c),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
geo-point_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-sep_wf,
not_wf,
geo-between_wf,
geo-between-symmetry,
geo-between-same-side
Rules used in proof :
instantiate,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
lambdaEquality,
productEquality,
sqequalRule,
because_Cache,
applyEquality,
voidElimination,
independent_pairFormation,
productElimination,
independent_functionElimination,
independent_isectElimination,
isectElimination,
isect_memberFormation,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}e:BasicGeometry. \mforall{}[A,B,C,D:Point]. (Colinear(A;C;D)) supposing (A \mneq{} B and A\_B\_C and A\_B\_D)
Date html generated:
2017_10_02-PM-06_19_49
Last ObjectModification:
2017_08_05-PM-04_14_14
Theory : euclidean!plane!geometry
Home
Index