Nuprl Lemma : rtan0
rtan(r0) = r0
Proof
Definitions occuring in Statement :
rtan: rtan(x),
req: x = y,
int-to-real: r(n),
natural_number: $n
Definitions unfolded in proof :
rtan: rtan(x),
member: t ∈ T,
uall: ∀[x:A]. B[x],
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,
uimplies: b supposing a,
nat_plus: ℕ+,
uiff: uiff(P;Q),
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
false: False,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
int-to-real_wf,
rless-int,
rless_wf,
rdiv_wf,
req-int-fractions2,
less_than_wf,
decidable__equal_int,
full-omega-unsat,
intformnot_wf,
intformeq_wf,
itermConstant_wf,
itermMultiply_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_formula_prop_wf,
rsin_wf,
rcos_wf,
req_functionality,
rdiv_functionality,
rsin0,
req_weakening,
rneq_functionality,
rcos0
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
because_Cache,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
sqequalRule,
inrFormation,
dependent_functionElimination,
productElimination,
independent_functionElimination,
independent_pairFormation,
imageMemberEquality,
hypothesisEquality,
baseClosed,
independent_isectElimination,
dependent_set_memberEquality,
unionElimination,
approximateComputation,
dependent_pairFormation,
lambdaEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
rtan(r0) = r0
Date html generated:
2018_05_22-PM-02_59_25
Last ObjectModification:
2017_10_21-PM-11_36_58
Theory : reals_2
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