Nuprl Lemma : 2-MachinPi4
2 * MachinPi4() = π/2
Proof
Definitions occuring in Statement :
MachinPi4: MachinPi4(),
halfpi: π/2,
int-rmul: k1 * a,
req: x = y,
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
prop: ℙ,
so_apply: x[s],
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
sq_stable: SqStable(P),
pi: π,
rdiv: (x/y),
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
top: Top
Lemmas referenced :
MachinPi4_wf,
set_wf,
real_wf,
req_wf,
rdiv_wf,
pi_wf,
int-to-real_wf,
rless-int,
rless_wf,
equal_wf,
int-rmul_wf,
rmul_wf,
halfpi_wf,
req_functionality,
int-rmul-req,
req_weakening,
sq_stable__req,
rmul_functionality,
rdiv_functionality,
rinv_wf2,
itermSubtract_wf,
itermMultiply_wf,
itermConstant_wf,
itermVar_wf,
req-iff-rsub-is-0,
req_transitivity,
rmul-rinv3,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_mul_lemma,
real_term_value_const_lemma,
real_term_value_var_lemma
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
introduction,
extract_by_obid,
hypothesis,
thin,
sqequalHypSubstitution,
isectElimination,
sqequalRule,
lambdaEquality,
hypothesisEquality,
natural_numberEquality,
independent_isectElimination,
inrFormation,
dependent_functionElimination,
because_Cache,
productElimination,
independent_functionElimination,
independent_pairFormation,
imageMemberEquality,
baseClosed,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
setElimination,
rename,
imageElimination,
approximateComputation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
2 * MachinPi4() = \mpi{}/2
Date html generated:
2018_05_22-PM-03_06_10
Last ObjectModification:
2017_10_27-AM-00_11_53
Theory : reals_2
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