Nuprl Lemma : P_point-sep_wf
∀[eu:EuclideanParPlane]. ∀P,Q:P_point(eu). (P_point-sep(eu;P;Q) ∈ ℙ)
Proof
Definitions occuring in Statement :
P_point-sep: P_point-sep(eu;P;Q),
P_point: P_point(eu),
euclidean-parallel-plane: EuclideanParPlane,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
P_point-sep: P_point-sep(eu;P;Q),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
exists_wf,
P_line_wf,
not_wf,
P_point-line-sep_wf,
P_point_wf,
euclidean-parallel-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
lambdaEquality,
productEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache
Latex:
\mforall{}[eu:EuclideanParPlane]. \mforall{}P,Q:P\_point(eu). (P\_point-sep(eu;P;Q) \mmember{} \mBbbP{})
Date html generated:
2019_10_16-PM-03_01_49
Last ObjectModification:
2018_08_09-PM-04_03_25
Theory : euclidean!plane!geometry
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