Nuprl Lemma : geo-between_functionality
∀e:EuclideanPlane. ∀a1,a2,b1,b2,c1,c2:Point. (a1 ≡ a2 ⇒ b1 ≡ b2 ⇒ c1 ≡ c2 ⇒ (a1_b1_c1 ⇐⇒ a2_b2_c2))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-eq: a ≡ b,
geo-between: a_b_c,
geo-point: Point,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
squash: ↓T,
and: P ∧ Q,
sq_stable: SqStable(P),
implies: P ⇒ Q,
euclidean-plane: EuclideanPlane,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
sq_stable__geo-axioms,
euclidean-plane_wf,
implies-geo-between_functionality
Rules used in proof :
imageElimination,
baseClosed,
imageMemberEquality,
sqequalRule,
productElimination,
independent_functionElimination,
hypothesisEquality,
rename,
setElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a1,a2,b1,b2,c1,c2:Point.
(a1 \mequiv{} a2 {}\mRightarrow{} b1 \mequiv{} b2 {}\mRightarrow{} c1 \mequiv{} c2 {}\mRightarrow{} (a1\_b1\_c1 \mLeftarrow{}{}\mRightarrow{} a2\_b2\_c2))
Date html generated:
2018_05_22-AM-11_53_12
Last ObjectModification:
2018_05_21-AM-01_13_12
Theory : euclidean!plane!geometry
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