Nuprl Lemma : eu-le_transitivity
∀e:EuclideanPlane. ∀[p,q,r:{p:Point| O_X_p} ]. (p ≤ r) supposing (q ≤ r and p ≤ q)
Proof
Definitions occuring in Statement :
eu-le: p ≤ q,
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
eu-X: X,
eu-O: O,
eu-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
eu-le: p ≤ q,
member: t ∈ T,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
euclidean-plane_wf,
eu-O_wf,
eu-between-eq_wf,
eu-point_wf,
set_wf,
eu-le_wf,
eu-between-eq-exchange4,
eu-between-eq-exchange3,
eu-between-eq-inner-trans,
eu-between-eq-symmetry,
eu-X_wf,
sq_stable__eu-between-eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
sqequalHypSubstitution,
cut,
lemma_by_obid,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
isectElimination,
hypothesis,
independent_functionElimination,
introduction,
because_Cache,
independent_isectElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
lambdaEquality
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[p,q,r:\{p:Point| O\_X\_p\} ]. (p \mleq{} r) supposing (q \mleq{} r and p \mleq{} q)
Date html generated:
2016_05_18-AM-06_37_23
Last ObjectModification:
2016_01_16-PM-10_30_30
Theory : euclidean!geometry
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