Nuprl Lemma : r2-lines-par_wf
∀[a,b,c,d:ℝ^2].  (r2-lines-par(a;b;c;d) ∈ ℙ)
Proof
Definitions occuring in Statement : 
r2-lines-par: r2-lines-par(a;b;c;d)
, 
real-vec: ℝ^n
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
natural_number: $n
Definitions unfolded in proof : 
prop: ℙ
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
false: False
, 
less_than': less_than'(a;b)
, 
and: P ∧ Q
, 
le: A ≤ B
, 
nat: ℕ
, 
r2-lines-par: r2-lines-par(a;b;c;d)
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
le_wf, 
false_wf, 
real-vec_wf, 
int-to-real_wf, 
line-det_wf, 
rneq_wf
Rules used in proof : 
because_Cache, 
isect_memberEquality, 
lambdaFormation, 
independent_pairFormation, 
dependent_set_memberEquality, 
equalitySymmetry, 
equalityTransitivity, 
axiomEquality, 
natural_numberEquality, 
hypothesis, 
hypothesisEquality, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
sqequalRule, 
cut, 
introduction, 
isect_memberFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}[a,b,c,d:\mBbbR{}\^{}2].    (r2-lines-par(a;b;c;d)  \mmember{}  \mBbbP{})
Date html generated:
2018_07_29-AM-09_47_11
Last ObjectModification:
2018_07_02-PM-03_11_24
Theory : reals!model!euclidean!geometry
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