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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