Nuprl Lemma : rexp0
e^r0 = r1
Proof
Definitions occuring in Statement :
rexp: e^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,
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
int_nzero: ℤ-o,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
prop: ℙ,
nequal: a ≠ b ∈ T ,
not: ¬A,
false: False,
guard: {T},
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
le: A ≤ B,
less_than': less_than'(a;b),
int_upper: {i...},
true: True,
rneq: x ≠ y,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
squash: ↓T,
rev_uimplies: rev_uimplies(P;Q),
decidable: Dec(P)
Lemmas referenced :
rexp-is-limit,
int-to-real_wf,
series-sum-constant,
ifthenelse_wf,
eq_int_wf,
real_wf,
nat_wf,
int-rdiv_wf,
fact_wf,
subtype_rel_sets,
less_than_wf,
nequal_wf,
nat_plus_properties,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
equal-wf-base,
int_subtype_base,
rnexp_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_upper_subtype_nat,
false_wf,
le_wf,
nequal-le-implies,
zero-add,
req_weakening,
series-sum_functionality,
rnexp_zero_lemma,
fact0_redex_lemma,
true_wf,
rdiv_wf,
rless-int,
rless_wf,
rmul_preserves_req,
req_wf,
rmul_wf,
req_functionality,
int-rdiv-req,
uiff_transitivity,
rmul-int,
rmul-ident-div,
int_upper_properties,
decidable__lt,
not-lt-2,
add_functionality_wrt_le,
add-commutes,
le-add-cancel,
nat_plus_wf,
rneq-int,
fact-non-zero,
int-rdiv_functionality,
rnexp0,
rdiv-zero,
series-sum-unique,
rexp_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,
setElimination,
rename,
hypothesisEquality,
applyEquality,
sqequalRule,
intEquality,
because_Cache,
independent_isectElimination,
setEquality,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
baseClosed,
unionElimination,
equalityElimination,
productElimination,
promote_hyp,
instantiate,
hypothesis_subsumption,
dependent_set_memberEquality,
cumulativity,
addLevel,
inrFormation,
imageMemberEquality,
multiplyEquality
Latex:
e\^{}r0 = r1
Date html generated:
2017_10_03-AM-09_30_12
Last ObjectModification:
2017_07_28-AM-07_49_03
Theory : reals
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