Nuprl Lemma : r2-unit-circle_wf
∀[p:ℝ^2]. (r2-unit-circle(p) ∈ ℙ)
Proof
Definitions occuring in Statement :
r2-unit-circle: r2-unit-circle(p),
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-unit-circle: r2-unit-circle(p),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T,
true: True
Lemmas referenced :
req_wf,
radd_wf,
rnexp_wf,
false_wf,
le_wf,
lelt_wf,
int-to-real_wf,
real-vec_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
hypothesis,
hypothesisEquality,
applyEquality,
because_Cache,
imageMemberEquality,
baseClosed,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[p:\mBbbR{}\^{}2]. (r2-unit-circle(p) \mmember{} \mBbbP{})
Date html generated:
2017_10_03-AM-10_50_51
Last ObjectModification:
2017_06_18-PM-01_23_37
Theory : reals
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