Nuprl Lemma : eu-between-eq-inner-trans
∀e:EuclideanPlane. ∀[a,b,c,d:Point]. (a_b_c) supposing (b_c_d and a_b_d)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
eu-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],
uimplies: b supposing a,
member: t ∈ T,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
implies: P ⇒ Q,
stable: Stable{P},
not: ¬A,
false: False,
prop: ℙ,
squash: ↓T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
true: True,
subtype_rel: A ⊆r B,
guard: {T}
Lemmas referenced :
sq_stable__eu-between-eq,
stable__eu-between-eq,
not_wf,
eu-between-eq_wf,
eu-point_wf,
euclidean-plane_wf,
eu-between-eq-def,
equal_wf,
eu-between_wf,
eu-between-trans,
stable__eu-between,
squash_wf,
true_wf,
euclidean-structure_wf,
iff_weakening_equal,
eu-between-same,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
isectElimination,
hypothesisEquality,
independent_functionElimination,
independent_isectElimination,
addLevel,
voidElimination,
levelHypothesis,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
productEquality,
independent_pairFormation,
equalitySymmetry,
equalityTransitivity,
applyEquality,
lambdaEquality,
universeEquality,
natural_numberEquality,
hyp_replacement,
dependent_set_memberEquality,
setEquality
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c,d:Point]. (a\_b\_c) supposing (b\_c\_d and a\_b\_d)
Date html generated:
2016_10_26-AM-07_40_59
Last ObjectModification:
2016_07_12-AM-08_07_10
Theory : euclidean!geometry
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