Nuprl Lemma : MachinPi4_wf
MachinPi4() ∈ {x:ℝ| x = (π/r(4))}
Proof
Definitions occuring in Statement :
MachinPi4: MachinPi4(),
pi: π,
rdiv: (x/y),
req: x = y,
int-to-real: r(n),
real: ℝ,
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
MachinPi4: MachinPi4(),
member: t ∈ T,
uall: ∀[x:A]. B[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,
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],
rneq: x ≠ y,
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
squash: ↓T,
nat_plus: ℕ+,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
atan_wf,
false_wf,
le_wf,
int-rdiv_wf,
subtype_base_sq,
int_subtype_base,
equal-wf-base,
true_wf,
nequal_wf,
int-to-real_wf,
set_wf,
real_wf,
req_wf,
arctangent_wf,
rsub_wf,
int-rmul_wf,
rdiv_wf,
pi_wf,
rless-int,
rless_wf,
equal_wf,
rabs_wf,
rleq-int-fractions2,
less_than_wf,
rleq_weakening_equal,
rleq_functionality,
rabs_functionality,
int-rdiv-req,
req_weakening,
rabs-of-nonneg,
rmul_wf,
req_functionality,
rsub_functionality,
int-rmul-req,
Machin-lemma,
arctangent_functionality,
req_inversion,
rmul_functionality
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
hypothesis,
hypothesisEquality,
because_Cache,
addLevel,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
baseClosed,
lambdaEquality,
setElimination,
rename,
inrFormation,
productElimination,
imageMemberEquality,
multiplyEquality
Latex:
MachinPi4() \mmember{} \{x:\mBbbR{}| x = (\mpi{}/r(4))\}
Date html generated:
2018_05_22-PM-03_06_05
Last ObjectModification:
2017_10_26-PM-03_49_47
Theory : reals_2
Home
Index