Nuprl Lemma : fps-elim-x-zero
∀[X:Type]. ∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀[x:X]. (0(x:=0) = 0 ∈ PowerSeries(X;r))
Proof
Definitions occuring in Statement :
fps-elim-x: f(x:=0)
,
fps-zero: 0
,
power-series: PowerSeries(X;r)
,
deq: EqDecider(T)
,
uall: ∀[x:A]. B[x]
,
universe: Type
,
equal: s = t ∈ T
,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
uimplies: b supposing a
,
all: ∀x:A. B[x]
,
fps-zero: 0
,
fps-coeff: f[b]
,
fps-elim-x: f(x:=0)
,
fps-elim: fps-elim(x)
,
implies: P
⇒ Q
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
ifthenelse: if b then t else f fi
,
crng: CRng
,
rng: Rng
,
bfalse: ff
,
exists: ∃x:A. B[x]
,
prop: ℙ
,
or: P ∨ Q
,
sq_type: SQType(T)
,
guard: {T}
,
bnot: ¬bb
,
assert: ↑b
,
false: False
,
not: ¬A
Lemmas referenced :
fps-ext,
fps-elim-x_wf,
fps-zero_wf,
bag-deq-member_wf,
bool_wf,
eqtt_to_assert,
assert-bag-deq-member,
rng_zero_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
bag-member_wf,
bag_wf,
crng_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
cumulativity,
hypothesis,
productElimination,
independent_isectElimination,
lambdaFormation,
sqequalRule,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
setElimination,
rename,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
independent_functionElimination,
voidElimination,
isect_memberEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[r:CRng]. \mforall{}[x:X]. (0(x:=0) = 0)
Date html generated:
2018_05_21-PM-09_59_30
Last ObjectModification:
2017_07_26-PM-06_33_54
Theory : power!series
Home
Index