Nuprl Lemma : rroot_functionality
∀[i:{2...}]. ∀[x:{x:ℝ| (↑isEven(i)) ⇒ (r0 ≤ x)} ]. ∀[y:ℝ]. rroot(i;x) = rroot(i;y) supposing x = y
Proof
Definitions occuring in Statement :
rroot: rroot(i;x),
rleq: x ≤ y,
req: x = y,
int-to-real: r(n),
real: ℝ,
isEven: isEven(n),
int_upper: {i...},
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
sq_stable: SqStable(P),
guard: {T},
squash: ↓T,
prop: ℙ,
int_upper: {i...},
so_lambda: λ2x.t[x],
and: P ∧ Q,
subtype_rel: A ⊆r B,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
so_apply: x[s],
all: ∀x:A. B[x],
uiff: uiff(P;Q),
or: P ∨ Q,
nat_plus: ℕ+,
decidable: Dec(P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
top: Top,
true: True
Lemmas referenced :
rnexp-req-iff,
less_than_wf,
le-add-cancel,
zero-add,
add-commutes,
add_functionality_wrt_le,
not-lt-2,
decidable__lt,
rnexp-req-iff-odd,
isOdd_wf,
assert_of_bor,
odd-or-even,
int_upper_wf,
req_witness,
equal_wf,
req_transitivity,
req_inversion,
sq_stable__req,
and_wf,
le_wf,
false_wf,
int_upper_subtype_nat,
rnexp_wf,
req_wf,
rleq_wf,
real_wf,
set_wf,
rroot_wf,
isEven_wf,
assert_wf,
rleq_weakening,
rleq_transitivity,
int-to-real_wf,
sq_stable__rleq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
setElimination,
thin,
rename,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
independent_functionElimination,
independent_isectElimination,
because_Cache,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
lambdaEquality,
productEquality,
functionEquality,
applyEquality,
dependent_set_memberEquality,
independent_pairFormation,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
setEquality,
isect_memberEquality,
unionElimination,
voidElimination,
voidEquality,
intEquality
Latex:
\mforall{}[i:\{2...\}]. \mforall{}[x:\{x:\mBbbR{}| (\muparrow{}isEven(i)) {}\mRightarrow{} (r0 \mleq{} x)\} ]. \mforall{}[y:\mBbbR{}]. rroot(i;x) = rroot(i;y) supposing x = y
Date html generated:
2016_05_18-AM-09_42_29
Last ObjectModification:
2016_01_17-AM-02_50_19
Theory : reals
Home
Index