Nuprl Lemma : sine0
sine(r0) = r0
Proof
Definitions occuring in Statement :
sine: sine(x),
req: x = y,
int-to-real: r(n),
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
int_nzero: ℤ-o,
so_lambda: λ2x.t[x],
so_apply: x[s],
nequal: a ≠ b ∈ T ,
guard: {T},
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
sine-is-limit,
int-to-real_wf,
series-sum-0,
nat_wf,
int-rmul_wf,
fastexp_wf,
int-rdiv_wf,
fact_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermMultiply_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_mul_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
subtype_rel_sets,
less_than_wf,
nequal_wf,
nat_plus_properties,
intformeq_wf,
intformless_wf,
int_formula_prop_eq_lemma,
int_formula_prop_less_lemma,
equal-wf-base,
int_subtype_base,
rnexp_wf,
req_weakening,
series-sum_functionality,
decidable__lt,
nat_plus_wf,
req_functionality,
int-rmul_functionality,
int-rdiv_functionality,
rnexp0,
rmul_wf,
req_wf,
rdiv_wf,
rneq-int,
fact-non-zero,
req-int,
decidable__equal_int,
req_transitivity,
int-rmul-req,
rmul_functionality,
int-rdiv-req,
uiff_transitivity,
rdiv-zero,
rmul-int,
series-sum-unique,
sine_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
hypothesis,
independent_functionElimination,
lambdaEquality,
minusEquality,
hypothesisEquality,
dependent_set_memberEquality,
addEquality,
multiplyEquality,
setElimination,
rename,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
applyEquality,
because_Cache,
setEquality,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
Error :applyLambdaEquality,
baseClosed,
productElimination
Latex:
sine(r0) = r0
Date html generated:
2016_10_26-AM-09_24_45
Last ObjectModification:
2016_08_29-AM-10_42_53
Theory : reals
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