Nuprl Lemma : rnexp_step
∀[x:ℝ]. ∀[n:ℕ+]. (x^n = (x^n - 1 * x))
Proof
Definitions occuring in Statement :
rnexp: x^k1,
req: x = y,
rmul: a * b,
real: ℝ,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
nat: ℕ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
rev_uimplies: rev_uimplies(P;Q),
subtract: n - m
Lemmas referenced :
req_witness,
rnexp_wf,
nat_plus_subtype_nat,
rmul_wf,
subtract_wf,
nat_plus_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
nat_plus_wf,
real_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
int-to-real_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
intformeq_wf,
int_formula_prop_eq_lemma,
req_weakening,
req_functionality,
rnexp_unroll,
int_subtype_base,
rnexp_zero_lemma,
rmul-one-both
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
dependent_set_memberEquality,
setElimination,
rename,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
because_Cache,
independent_functionElimination,
lambdaFormation,
equalityElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
instantiate,
cumulativity
Latex:
\mforall{}[x:\mBbbR{}]. \mforall{}[n:\mBbbN{}\msupplus{}]. (x\^{}n = (x\^{}n - 1 * x))
Date html generated:
2017_10_03-AM-08_31_43
Last ObjectModification:
2017_07_28-AM-07_27_14
Theory : reals
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