Nuprl Lemma : cosh0
cosh(r0) = r1
Proof
Definitions occuring in Statement :
cosh: cosh(x),
req: x = y,
int-to-real: r(n),
natural_number: $n
Definitions unfolded in proof :
cosh: cosh(x),
member: t ∈ T,
uall: ∀[x:A]. B[x],
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2,
top: Top,
rneq: x ≠ y,
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
rdiv: (x/y)
Lemmas referenced :
int-rdiv_wf,
subtype_base_sq,
int_subtype_base,
equal-wf-base,
true_wf,
nequal_wf,
radd_wf,
expr_wf,
int-to-real_wf,
real_wf,
req_wf,
rexp_wf,
rminus_wf,
rmul_wf,
rminus-zero,
itermSubtract_wf,
itermAdd_wf,
itermVar_wf,
itermMultiply_wf,
itermConstant_wf,
req-iff-rsub-is-0,
req_functionality,
int-rdiv_functionality,
radd_functionality,
expr-req,
req_weakening,
req_transitivity,
rexp_functionality,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_add_lemma,
real_term_value_var_lemma,
real_term_value_mul_lemma,
real_term_value_const_lemma,
rdiv_wf,
rless-int,
rless_wf,
int-rdiv-req,
rdiv_functionality,
rmul_functionality,
rexp0,
rmul_preserves_req,
rinv_wf2,
decidable__equal_int,
full-omega-unsat,
intformnot_wf,
intformeq_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,
rmul_comm,
int-rinv-cancel2,
rmul-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
addLevel,
lambdaFormation,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
baseClosed,
hypothesisEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
sqequalRule,
because_Cache,
productElimination,
approximateComputation,
int_eqEquality,
isect_memberEquality,
voidEquality,
inrFormation,
independent_pairFormation,
imageMemberEquality,
unionElimination,
dependent_pairFormation
Latex:
cosh(r0) = r1
Date html generated:
2017_10_04-PM-10_40_22
Last ObjectModification:
2017_06_21-PM-02_36_56
Theory : reals_2
Home
Index