Nuprl Lemma : small-ctrex1_wf
small-ctrex1() ∈ ℝ
Proof
Definitions occuring in Statement : 
small-ctrex1: small-ctrex1()
, 
real: ℝ
, 
member: t ∈ T
Definitions unfolded in proof : 
small-ctrex1: small-ctrex1()
, 
uiff: uiff(P;Q)
, 
nat_plus: ℕ+
, 
rev_implies: P 
⇐ Q
, 
iff: P 
⇐⇒ Q
, 
or: P ∨ Q
, 
rneq: x ≠ y
, 
guard: {T}
, 
all: ∀x:A. B[x]
, 
sq_type: SQType(T)
, 
uimplies: b supposing a
, 
nequal: a ≠ b ∈ T 
, 
int_nzero: ℤ-o
, 
prop: ℙ
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
false: False
, 
le: A ≤ B
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
and: P ∧ Q
, 
member: t ∈ T
, 
true: True
, 
efficient-exp-ext, 
fastexp: i^n
, 
less_than': less_than'(a;b)
, 
squash: ↓T
, 
less_than: a < b
, 
rev_uimplies: rev_uimplies(P;Q)
, 
subtype_rel: A ⊆r B
, 
exists: ∃x:A. B[x]
, 
reg-seq-mul: reg-seq-mul(x;y)
, 
lt_int: i <z j
, 
bnot: ¬bb
, 
le_int: i ≤z j
, 
rroot-odd: rroot-odd(i;x)
, 
canonical-bound: canonical-bound(r)
, 
imax: imax(a;b)
, 
bfalse: ff
, 
rmul: a * b
, 
rminus: -(x)
, 
genrec-ap: genrec-ap, 
primrec: primrec(n;b;c)
, 
exp: i^n
, 
integer-nth-root-ext, 
iroot: iroot(n;x)
, 
it: ⋅
, 
nil: []
, 
int-rdiv: (a)/k1
, 
absval: |i|
, 
rabs: |x|
, 
subtract: n - m
, 
rroot-abs: rroot-abs(i;x)
, 
btrue: tt
, 
modulus: a mod n
, 
eq_int: (i =z j)
, 
isEven: isEven(n)
, 
ifthenelse: if b then t else f fi 
, 
rroot: rroot(i;x)
, 
rsub: x - y
, 
cons: [a / b]
, 
cbv_list_accum: cbv_list_accum(x,a.f[x; a];y;L)
, 
reg-seq-list-add: reg-seq-list-add(L)
, 
accelerate: accelerate(k;f)
, 
radd: a + b
, 
un-ctrex1: un-ctrex1(x)
, 
int-to-real: r(n)
Lemmas referenced : 
efficient-exp-ext, 
integer-nth-root-ext, 
equal-wf-base, 
rless-iff2, 
rleq_weakening_rless, 
int-rdiv-req, 
req_weakening, 
rleq_functionality, 
fastexp_wf, 
false_wf, 
le_wf, 
un-ctrex1_wf, 
int-rdiv_wf, 
subtype_base_sq, 
int_subtype_base, 
true_wf, 
nequal_wf, 
rleq_wf, 
int-to-real_wf, 
rdiv_wf, 
rless-int, 
rless_wf, 
rleq-int-fractions2, 
less_than_wf
Rules used in proof : 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution, 
multiplyEquality, 
productElimination, 
inrFormation, 
minusEquality, 
voidElimination, 
independent_functionElimination, 
equalitySymmetry, 
equalityTransitivity, 
dependent_functionElimination, 
independent_isectElimination, 
intEquality, 
cumulativity, 
instantiate, 
addLevel, 
because_Cache, 
baseClosed, 
imageMemberEquality, 
introduction, 
hypothesisEquality, 
hypothesis, 
lambdaFormation, 
dependent_set_memberEquality, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
lemma_by_obid, 
natural_numberEquality, 
independent_pairFormation, 
sqequalRule, 
cut, 
applyEquality, 
addEquality, 
dependent_pairFormation
Latex:
small-ctrex1()  \mmember{}  \mBbbR{}
Date html generated:
2016_05_18-AM-10_48_15
Last ObjectModification:
2016_01_17-AM-00_25_40
Theory : reals
Home
Index