Nuprl Lemma : un-ctrex1_wf
∀[x:{x:ℝ| r(-1) ≤ x} ]. (un-ctrex1(x) ∈ ℝ)
Proof
Definitions occuring in Statement :
un-ctrex1: un-ctrex1(x),
rleq: x ≤ y,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
minus: -n,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
un-ctrex1: un-ctrex1(x),
int_upper: {i...},
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_uimplies: rev_uimplies(P;Q),
rge: x ≥ y,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
isEven: isEven(n),
modulus: a mod n,
absval: |i|,
eq_int: (i =z j),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff
Lemmas referenced :
radd_wf,
rsub_wf,
rroot_wf,
false_wf,
le_wf,
rmul_wf,
int-to-real_wf,
real_wf,
assert_wf,
isEven_wf,
rleq_wf,
req_wf,
rnexp_wf,
int-rdiv_wf,
subtype_base_sq,
int_subtype_base,
equal_wf,
true_wf,
nequal_wf,
set_wf,
rleq_functionality_wrt_implies,
rleq_weakening_equal,
radd_functionality_wrt_rleq,
rleq-int,
rleq_functionality,
req_weakening,
radd-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
hypothesis,
hypothesisEquality,
applyEquality,
because_Cache,
lambdaEquality,
setEquality,
productEquality,
functionEquality,
addLevel,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
axiomEquality,
minusEquality,
addEquality,
productElimination,
callbyvalueReduce,
sqleReflexivity
Latex:
\mforall{}[x:\{x:\mBbbR{}| r(-1) \mleq{} x\} ]. (un-ctrex1(x) \mmember{} \mBbbR{})
Date html generated:
2016_05_18-AM-10_47_47
Last ObjectModification:
2015_12_27-PM-10_46_31
Theory : reals
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