Nuprl Lemma : r2-line-sep_wf
∀l,m:r2-line. (r2-line-sep(l;m) ∈ ℙ)
Proof
Definitions occuring in Statement :
r2-line-sep: r2-line-sep(l;m),
r2-line: r2-line,
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
pi2: snd(t),
pi1: fst(t),
r2-line: r2-line,
so_lambda: λ2x.t[x],
prop: ℙ,
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
uall: ∀[x:A]. B[x],
r2-line-sep: r2-line-sep(l;m),
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
r2-line_wf,
rneq_wf,
int-to-real_wf,
r2-det_wf,
req_wf,
le_wf,
false_wf,
real-vec_wf,
exists_wf
Rules used in proof :
because_Cache,
productElimination,
productEquality,
lambdaEquality,
hypothesisEquality,
hypothesis,
independent_pairFormation,
natural_numberEquality,
dependent_set_memberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
sqequalRule,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}l,m:r2-line. (r2-line-sep(l;m) \mmember{} \mBbbP{})
Date html generated:
2018_07_29-AM-09_46_59
Last ObjectModification:
2018_07_02-PM-04_05_16
Theory : reals!model!euclidean!geometry
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