Nuprl Lemma : fps-deriv-ucont
∀[X:Type]. ∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀x:X. fps-ucont(X;eq;r;f.df/dx)
Proof
Definitions occuring in Statement :
fps-deriv: df/dx,
fps-ucont: fps-ucont(X;eq;r;f.G[f]),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
fps-ucont: fps-ucont(X;eq;r;f.G[f]),
exists: ∃x:A. B[x],
member: t ∈ T,
fps-restrict: fps-restrict(eq;r;f;d),
fps-deriv: df/dx,
fps-coeff: f[b],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
ifthenelse: if b then t else f fi ,
infix_ap: x f y,
crng: CRng,
rng: Rng,
subtype_rel: A ⊆r B,
nat: ℕ,
power-series: PowerSeries(X;r),
bfalse: ff,
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
cons-bag_wf,
deq-sub-bag_wf,
bool_wf,
eqtt_to_assert,
assert-deq-sub-bag,
rng_times_wf,
int-to-ring_wf,
bag-count_wf,
nat_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
sub-bag_wf,
sub-bag_weakening,
power-series_wf,
all_wf,
rng_car_wf,
fps-coeff_wf,
fps-deriv_wf,
fps-restrict_wf,
bag_wf,
crng_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
dependent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
setElimination,
rename,
addEquality,
lambdaEquality,
natural_numberEquality,
promote_hyp,
instantiate,
cumulativity,
voidElimination,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[r:CRng]. \mforall{}x:X. fps-ucont(X;eq;r;f.df/dx)
Date html generated:
2018_05_21-PM-10_16_05
Last ObjectModification:
2018_05_19-PM-04_17_17
Theory : power!series
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