Nuprl Lemma : not-not-double-pasch
∀e:BasicGeometry. ∀a,b,c,a',b',p:Point. (a_b_c ⇒ a'_b'_c ⇒ a_p_a' ⇒ (¬¬(∃q:Point. (p_q_c ∧ b_q_b'))))
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-between: a_b_c,
geo-point: Point,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
exists: ∃x:A. B[x],
so_apply: x[s],
and: P ∧ Q,
so_lambda: λ2x.t[x],
guard: {T},
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
false: False,
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x],
cand: A c∧ B
Lemmas referenced :
double-negation-hyp-elim,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
exists_wf,
not_wf,
geo-between_wf,
geo-between-symmetry,
Error :not-not-inner-pasch,
geo-between-exchange4,
geo-between-exchange3,
geo-between-inner-trans
Rules used in proof :
productElimination,
productEquality,
lambdaEquality,
instantiate,
voidElimination,
independent_functionElimination,
sqequalRule,
applyEquality,
dependent_set_memberEquality,
hypothesis,
independent_isectElimination,
isectElimination,
hypothesisEquality,
because_Cache,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
thin,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_pairFormation,
dependent_pairFormation
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,a',b',p:Point.
(a\_b\_c {}\mRightarrow{} a'\_b'\_c {}\mRightarrow{} a\_p\_a' {}\mRightarrow{} (\mneg{}\mneg{}(\mexists{}q:Point. (p\_q\_c \mwedge{} b\_q\_b'))))
Date html generated:
2017_10_02-PM-06_15_46
Last ObjectModification:
2017_08_05-PM-04_12_22
Theory : euclidean!plane!geometry
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