Nuprl Lemma : geo-between-exchange4
∀e:BasicGeometry-. ∀[a,b,c,d:Point]. (a_b_d) supposing (a_c_d and a_b_c)
Proof
Definitions occuring in Statement :
basic-geometry-: BasicGeometry-,
geo-between: a_b_c,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
geo-eq: a ≡ b,
false: False,
or: P ∨ Q,
not: ¬A,
stable: Stable{P},
implies: P ⇒ Q,
basic-geometry-: BasicGeometry-,
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
member: t ∈ T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
minimal-not-not-excluded-middle,
geo-eq_weakening,
geo-between_functionality,
minimal-double-negation-hyp-elim,
not_wf,
geo-sep_wf,
or_wf,
false_wf,
stable__geo-between,
geo-point_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry-_wf,
subtype_rel_transitivity,
basic-geometry--subtype,
geo-between_wf,
geo-between-outer-trans,
geo-between-exchange3,
geo-between-inner-trans,
geo-between-symmetry,
geo-sep-sym
Rules used in proof :
productElimination,
voidElimination,
unionElimination,
independent_functionElimination,
functionEquality,
rename,
setElimination,
dependent_functionElimination,
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry-. \mforall{}[a,b,c,d:Point]. (a\_b\_d) supposing (a\_c\_d and a\_b\_c)
Date html generated:
2017_10_02-PM-04_51_37
Last ObjectModification:
2017_08_05-AM-09_08_22
Theory : euclidean!plane!geometry
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