Nuprl Lemma : rnexp-add
∀[n,m:ℕ]. ∀[x:ℝ]. ((x^n * x^m) = x^n + m)
Proof
Definitions occuring in Statement :
rnexp: x^k1,
req: x = y,
rmul: a * b,
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
add: n + m
Definitions unfolded in proof :
req_int_terms: t1 ≡ t2,
so_apply: x[s],
so_lambda: λ2x.t[x],
nequal: a ≠ b ∈ T ,
assert: ↑b,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
bfalse: ff,
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
rev_uimplies: rev_uimplies(P;Q),
uiff: uiff(P;Q),
prop: ℙ,
and: P ∧ Q,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
ge: i ≥ j ,
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
real_term_value_const_lemma,
real_term_value_var_lemma,
real_term_value_mul_lemma,
real_term_value_sub_lemma,
real_polynomial_null,
req_inversion,
req-iff-rsub-is-0,
itermMultiply_wf,
general_arith_equation1,
rmul_comm,
rmul-one,
decidable__equal_int,
int_subtype_base,
set_subtype_base,
rnexp_unroll,
rmul_functionality,
int_formula_prop_eq_lemma,
intformeq_wf,
neg_assert_of_eq_int,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
assert_of_eq_int,
eqtt_to_assert,
bool_wf,
eq_int_wf,
req_functionality,
req_weakening,
zero-add,
rmul-identity1,
int-to-real_wf,
int_term_value_subtract_lemma,
itermSubtract_wf,
subtract_wf,
rnexp_zero_lemma,
less_than_wf,
ge_wf,
int_formula_prop_less_lemma,
intformless_wf,
nat_wf,
real_wf,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
rnexp_wf,
rmul_wf,
req_witness
Rules used in proof :
cumulativity,
instantiate,
promote_hyp,
equalitySymmetry,
equalityTransitivity,
equalityElimination,
productElimination,
lambdaFormation,
intWeakElimination,
because_Cache,
independent_pairFormation,
sqequalRule,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
unionElimination,
natural_numberEquality,
dependent_functionElimination,
rename,
setElimination,
addEquality,
dependent_set_memberEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n,m:\mBbbN{}]. \mforall{}[x:\mBbbR{}]. ((x\^{}n * x\^{}m) = x\^{}n + m)
Date html generated:
2018_05_22-PM-01_32_46
Last ObjectModification:
2018_05_21-AM-00_07_23
Theory : reals
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