Nuprl Lemma : rtan-pi-over-4
rtan((π/r(4))) = r1
Proof
Definitions occuring in Statement :
rtan: rtan(x),
pi: π,
rdiv: (x/y),
req: x = y,
int-to-real: r(n),
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
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,
uall: ∀[x:A]. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
rneq: x ≠ y,
or: P ∨ Q,
rtan: rtan(x),
le: A ≤ B,
false: False,
not: ¬A,
guard: {T},
rless: x < y,
sq_exists: ∃x:A [B[x]],
nat_plus: ℕ+,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
rdiv: (x/y),
uiff: uiff(P;Q),
req_int_terms: t1 ≡ t2,
rev_uimplies: rev_uimplies(P;Q),
rat_term_to_real: rat_term_to_real(f;t),
rtermConstant: "const",
rat_term_ind: rat_term_ind,
pi1: fst(t),
rtermDivide: num "/" denom,
rtermVar: rtermVar(var),
pi2: snd(t)
Lemmas referenced :
rsqrt-positive,
rless-int,
int-to-real_wf,
rless_wf,
rmul_preserves_rless,
rdiv_wf,
rsqrt_wf,
rmul_wf,
rleq-int,
istype-false,
rleq_wf,
itermSubtract_wf,
itermMultiply_wf,
itermConstant_wf,
itermVar_wf,
rinv_wf2,
rcos_wf,
pi_wf,
rsin_wf,
rneq-int,
nat_plus_properties,
full-omega-unsat,
intformeq_wf,
istype-int,
int_formula_prop_eq_lemma,
istype-void,
int_term_value_constant_lemma,
int_formula_prop_wf,
rless_functionality,
req_transitivity,
rmul-rinv,
req-iff-rsub-is-0,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_mul_lemma,
real_term_value_const_lemma,
real_term_value_var_lemma,
req_weakening,
rcos-pi-over-4,
req_functionality,
rdiv_functionality,
rsin-pi-over-4,
assert-rat-term-eq2,
rtermDivide_wf,
rtermVar_wf,
rtermConstant_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
natural_numberEquality,
productElimination,
independent_functionElimination,
sqequalRule,
independent_pairFormation,
imageMemberEquality,
hypothesisEquality,
baseClosed,
hypothesis,
dependent_set_memberEquality_alt,
isectElimination,
universeIsType,
because_Cache,
applyEquality,
independent_isectElimination,
inrFormation_alt,
closedConclusion,
lambdaFormation_alt,
setElimination,
rename,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
isect_memberEquality_alt,
voidElimination,
equalityIstype,
sqequalBase,
equalitySymmetry,
int_eqEquality,
inhabitedIsType,
equalityTransitivity
Latex:
rtan((\mpi{}/r(4))) = r1
Date html generated:
2019_10_30-AM-11_44_16
Last ObjectModification:
2019_04_03-AM-00_21_35
Theory : reals_2
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