Nuprl Lemma : eu-lt_wf
∀[e:EuclideanPlane]. ∀[p,q:{p:Point| O_X_p} ]. (p < q ∈ ℙ)
Proof
Definitions occuring in Statement :
eu-lt: p < q,
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
eu-X: X,
eu-O: O,
eu-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eu-lt: p < q,
prop: ℙ,
and: P ∧ Q,
euclidean-plane: EuclideanPlane,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
eu-le_wf,
eu-between-eq_wf,
eu-O_wf,
eu-X_wf,
not_wf,
equal_wf,
eu-point_wf,
set_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
sqequalRule,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
dependent_set_memberEquality,
hypothesis,
dependent_functionElimination,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
isect_memberEquality
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[p,q:\{p:Point| O\_X\_p\} ]. (p < q \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-06_37_29
Last ObjectModification:
2015_12_28-AM-09_25_11
Theory : euclidean!geometry
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