Nuprl Lemma : eu-eqt
∀e:EuclideanPlane. ∀a,b,c:{p:Point| O_X_p} .
(((a = b ∈ {p:Point| O_X_p} ) ∧ (b = c ∈ {p:Point| O_X_p} )) ⇒ (a = c ∈ {p:Point| O_X_p} ))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
eu-X: X,
eu-O: O,
eu-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
euclidean-plane: EuclideanPlane,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
and_wf,
equal_wf,
eu-point_wf,
eu-between-eq_wf,
eu-O_wf,
eu-X_wf,
set_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
equalityTransitivity,
hypothesis,
lemma_by_obid,
isectElimination,
setEquality,
setElimination,
rename,
hypothesisEquality,
dependent_functionElimination,
sqequalRule,
lambdaEquality
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c:\{p:Point| O\_X\_p\} . (((a = b) \mwedge{} (b = c)) {}\mRightarrow{} (a = c))
Date html generated:
2016_05_18-AM-06_43_52
Last ObjectModification:
2015_12_28-AM-09_21_41
Theory : euclidean!geometry
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