Nuprl Lemma : r2-left_wf
∀[p,q,r:ℝ^2]. (r2-left(p;q;r) ∈ ℙ)
Proof
Definitions occuring in Statement :
r2-left: r2-left(p;q;r),
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
r2-left: r2-left(p;q;r),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
rless_wf,
int-to-real_wf,
r2-det_wf,
real-vec_wf,
false_wf,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
independent_pairFormation,
lambdaFormation,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[p,q,r:\mBbbR{}\^{}2]. (r2-left(p;q;r) \mmember{} \mBbbP{})
Date html generated:
2017_10_03-AM-11_47_45
Last ObjectModification:
2017_04_11-PM-05_34_02
Theory : reals
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