Nuprl Lemma : faster-sin_wf
∀[x:ℝ]. (faster-sin(x) ∈ {y:ℝ| y = rsin(x)} )
Proof
Definitions occuring in Statement :
faster-sin: faster-sin(x),
rsin: rsin(x),
req: x = y,
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
faster-sin: faster-sin(x),
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
rneq: x ≠ y,
or: P ∨ Q,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
and: P ∧ Q,
has-value: (a)↓
Lemmas referenced :
int-rdiv_wf,
subtype_base_sq,
int_subtype_base,
istype-int,
nequal_wf,
rdiv_wf,
MachinPi4_wf,
MachinPi4-positive,
rless_wf,
int-to-real_wf,
istype-less_than,
value-type-has-value,
int-value-type,
rsin-shift-MachinPi4,
rsin_wf,
rsub_wf,
int-rmul_wf,
req_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
divideEquality,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality_alt,
natural_numberEquality,
lambdaFormation_alt,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
equalityIstype,
baseClosed,
sqequalBase,
universeIsType,
hypothesisEquality,
lambdaEquality_alt,
setElimination,
rename,
inhabitedIsType,
sqequalRule,
inrFormation_alt,
because_Cache,
closedConclusion,
independent_pairFormation,
imageMemberEquality,
callbyvalueReduce,
multiplyEquality,
axiomEquality
Latex:
\mforall{}[x:\mBbbR{}]. (faster-sin(x) \mmember{} \{y:\mBbbR{}| y = rsin(x)\} )
Date html generated:
2019_10_31-AM-06_08_20
Last ObjectModification:
2019_01_29-PM-03_45_53
Theory : reals_2
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