Nuprl Lemma : rnexp-add1
∀[n:ℕ]. ∀[x:ℝ]. (x^n + 1 = (x * x^n))
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,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ,
le: A ≤ B,
less_than': less_than'(a;b),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rnexp_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
rmul_wf,
real_wf,
nat_wf,
false_wf,
rmul_comm,
req_functionality,
req_transitivity,
req_inversion,
rnexp-add,
rmul_functionality,
req_weakening,
rnexp1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
because_Cache,
lambdaFormation,
productElimination
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x:\mBbbR{}]. (x\^{}n + 1 = (x * x\^{}n))
Date html generated:
2018_05_22-PM-01_32_53
Last ObjectModification:
2017_10_25-PM-03_51_37
Theory : reals
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