Nuprl Lemma : rcos-pi
rcos(π) = -(r1)
Proof
Definitions occuring in Statement :
pi: π,
rcos: rcos(x),
req: x = y,
rminus: -(x),
int-to-real: r(n),
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
uiff: uiff(P;Q),
all: ∀x:A. B[x],
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
top: Top
Lemmas referenced :
rcos-shift-pi,
int-to-real_wf,
rcos_wf,
radd_wf,
pi_wf,
rminus_wf,
itermSubtract_wf,
itermAdd_wf,
itermConstant_wf,
itermVar_wf,
itermMinus_wf,
req_wf,
squash_wf,
true_wf,
real_wf,
rminus-int,
subtype_rel_self,
iff_weakening_equal,
req_functionality,
req_weakening,
rminus_functionality,
rcos0,
rcos_functionality,
req-iff-rsub-is-0,
real_polynomial_null,
istype-int,
real_term_value_sub_lemma,
istype-void,
real_term_value_add_lemma,
real_term_value_const_lemma,
real_term_value_var_lemma,
real_term_value_minus_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
because_Cache,
minusEquality,
applyEquality,
lambdaEquality_alt,
imageElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
inhabitedIsType,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_functionElimination,
approximateComputation,
int_eqEquality,
isect_memberEquality_alt,
voidElimination
Latex:
rcos(\mpi{}) = -(r1)
Date html generated:
2019_10_30-AM-11_43_45
Last ObjectModification:
2019_06_10-PM-05_27_20
Theory : reals_2
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