Nuprl Lemma : stable__eu-between-eq
∀e:EuclideanStructure. ∀[a,b,c:Point]. Stable{a_b_c}
Proof
Definitions occuring in Statement :
eu-between-eq: a_b_c,
eu-point: Point,
euclidean-structure: EuclideanStructure,
stable: Stable{P},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
stable: Stable{P},
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
cand: A c∧ B
Lemmas referenced :
not_wf,
eu-between-eq_wf,
eu-between-eq-def,
and_wf,
equal_wf,
eu-point_wf,
eu-between_wf,
dneg_elim_a,
euclidean-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
lemma_by_obid,
isectElimination,
hypothesis,
rename,
productElimination,
independent_functionElimination,
impliesFunctionality,
because_Cache,
promote_hyp,
inlFormation,
independent_pairFormation
Latex:
\mforall{}e:EuclideanStructure. \mforall{}[a,b,c:Point]. Stable\{a\_b\_c\}
Date html generated:
2016_05_18-AM-06_33_02
Last ObjectModification:
2015_12_28-AM-09_28_24
Theory : euclidean!geometry
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