Nuprl Lemma : circle-param_wf
∀[t:ℝ]. (circle-param(t) ∈ {p:ℝ^2| r2-unit-circle(p)} )
Proof
Definitions occuring in Statement : 
circle-param: circle-param(t)
, 
r2-unit-circle: r2-unit-circle(p)
, 
real-vec: ℝ^n
, 
real: ℝ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
set: {x:A| B[x]} 
, 
natural_number: $n
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
and: P ∧ Q
, 
uiff: uiff(P;Q)
, 
uimplies: b supposing a
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
implies: P 
⇒ Q
, 
less_than: a < b
, 
squash: ↓T
, 
less_than': less_than'(a;b)
, 
true: True
, 
rge: x ≥ y
, 
guard: {T}
, 
circle-param: circle-param(t)
, 
real-vec: ℝ^n
, 
int_seg: {i..j-}
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
ifthenelse: if b then t else f fi 
, 
rneq: x ≠ y
, 
or: P ∨ Q
, 
bfalse: ff
, 
exists: ∃x:A. B[x]
, 
sq_type: SQType(T)
, 
bnot: ¬bb
, 
assert: ↑b
, 
false: False
, 
r2-unit-circle: r2-unit-circle(p)
, 
eq_int: (i =z j)
, 
nat: ℕ
, 
le: A ≤ B
, 
not: ¬A
, 
rev_uimplies: rev_uimplies(P;Q)
, 
rdiv: (x/y)
, 
req_int_terms: t1 ≡ t2
, 
top: Top
Lemmas referenced : 
square-nonneg, 
trivial-rleq-radd, 
int-to-real_wf, 
rmul_wf, 
r2-unit-circle_wf, 
real_wf, 
radd_wf, 
rless-int, 
rless_functionality_wrt_implies, 
rleq_weakening_equal, 
eq_int_wf, 
bool_wf, 
eqtt_to_assert, 
assert_of_eq_int, 
rdiv_wf, 
rsub_wf, 
rless_wf, 
eqff_to_assert, 
equal_wf, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_subtype_base, 
assert-bnot, 
neg_assert_of_eq_int, 
int_seg_wf, 
rnexp_wf, 
false_wf, 
le_wf, 
req_functionality, 
radd_functionality, 
rnexp2, 
req_weakening, 
rmul_preserves_req, 
rinv_wf2, 
itermSubtract_wf, 
itermMultiply_wf, 
itermAdd_wf, 
itermConstant_wf, 
itermVar_wf, 
req-iff-rsub-is-0, 
rmul-identity1, 
req_transitivity, 
rmul-rinv3, 
rmul_functionality, 
rinv-mul-as-rdiv, 
rinv-as-rdiv, 
real_polynomial_null, 
real_term_value_sub_lemma, 
real_term_value_mul_lemma, 
real_term_value_add_lemma, 
real_term_value_const_lemma, 
real_term_value_var_lemma, 
rmul-rinv
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
natural_numberEquality, 
productElimination, 
independent_isectElimination, 
dependent_set_memberEquality, 
sqequalRule, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
because_Cache, 
dependent_functionElimination, 
independent_functionElimination, 
independent_pairFormation, 
imageMemberEquality, 
baseClosed, 
lambdaEquality, 
setElimination, 
rename, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
inrFormation, 
dependent_pairFormation, 
promote_hyp, 
instantiate, 
cumulativity, 
voidElimination, 
approximateComputation, 
int_eqEquality, 
intEquality, 
isect_memberEquality, 
voidEquality
Latex:
\mforall{}[t:\mBbbR{}].  (circle-param(t)  \mmember{}  \{p:\mBbbR{}\^{}2|  r2-unit-circle(p)\}  )
Date html generated:
2017_10_03-AM-10_51_29
Last ObjectModification:
2017_06_18-PM-01_24_17
Theory : reals
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