Nuprl Lemma : rcos-half-pi
rcos(π/2(slower)) = r0
Proof
Definitions occuring in Statement :
half-pi: π/2(slower),
rcos: rcos(x),
req: x = y,
int-to-real: r(n),
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
guard: {T},
le: A ≤ B,
less_than': less_than'(a;b)
Lemmas referenced :
rcos-seq-converges-to-half-pi,
total-function-limit,
rcos_wf,
real_wf,
half-pi_wf,
rcos-seq_wf,
nat_wf,
req_wf,
req_weakening,
req_functionality,
rcos_functionality,
radd-limit,
radd_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
converges-to_functionality,
req_inversion,
rcos-seq-step,
limit-shift,
false_wf,
unique-limit,
radd-preserves-req,
rminus_wf,
rmul_wf,
int-to-real_wf,
uiff_transitivity,
req_transitivity,
radd_functionality,
rminus-as-rmul,
rmul-identity1,
rmul-distrib2,
radd-assoc,
rmul_functionality,
radd-int,
rmul-zero-both,
radd-zero-both
Rules used in proof :
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
sqequalRule,
lambdaEquality,
isectElimination,
hypothesisEquality,
independent_functionElimination,
lambdaFormation,
because_Cache,
independent_isectElimination,
productElimination,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
minusEquality
Latex:
rcos(\mpi{}/2(slower)) = r0
Date html generated:
2016_10_26-PM-00_20_36
Last ObjectModification:
2016_09_12-PM-05_42_04
Theory : reals_2
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