Nuprl Lemma : P_line-sep_wf
∀[eu:EuclideanParPlane]. ∀[l,m:P_line(eu)]. (P_line-sep(eu;l;m) ∈ ℙ)
Proof
Definitions occuring in Statement :
P_line-sep: P_line-sep(eu;L;M),
P_line: P_line(eu),
euclidean-parallel-plane: EuclideanParPlane,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
P_line-sep: P_line-sep(eu;L;M),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
exists_wf,
P_point_wf,
not_wf,
P_point-line-sep_wf,
P_line_wf,
euclidean-parallel-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
lambdaEquality,
productEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[eu:EuclideanParPlane]. \mforall{}[l,m:P\_line(eu)]. (P\_line-sep(eu;l;m) \mmember{} \mBbbP{})
Date html generated:
2019_10_16-PM-03_02_46
Last ObjectModification:
2018_08_08-PM-07_08_49
Theory : euclidean!plane!geometry
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