Nuprl Lemma : exp_step
∀[n:ℕ+]. ∀[i:ℤ].  (i^n ~ i * i^n - 1)
Proof
Definitions occuring in Statement : 
exp: i^n
, 
nat_plus: ℕ+
, 
uall: ∀[x:A]. B[x]
, 
multiply: n * m
, 
subtract: n - m
, 
natural_number: $n
, 
int: ℤ
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
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
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
squash: ↓T
, 
subtract: n - m
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
true: True
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
sq_type: SQType(T)
Lemmas referenced : 
exp_add, 
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, 
false_wf, 
equal_wf, 
squash_wf, 
true_wf, 
exp_wf2, 
nat_wf, 
add-associates, 
add-swap, 
add-commutes, 
zero-add, 
le_weakening2, 
mul-commutes, 
subtract-add-cancel, 
exp1, 
iff_weakening_equal, 
subtype_base_sq, 
int_subtype_base, 
nat_plus_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
dependent_set_memberEquality, 
setElimination, 
rename, 
hypothesisEquality, 
hypothesis, 
natural_numberEquality, 
dependent_functionElimination, 
unionElimination, 
independent_isectElimination, 
dependent_pairFormation, 
lambdaEquality, 
int_eqEquality, 
intEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
sqequalRule, 
independent_pairFormation, 
computeAll, 
lambdaFormation, 
because_Cache, 
hyp_replacement, 
equalitySymmetry, 
applyEquality, 
imageElimination, 
equalityTransitivity, 
universeEquality, 
minusEquality, 
imageMemberEquality, 
baseClosed, 
multiplyEquality, 
productElimination, 
independent_functionElimination, 
instantiate, 
cumulativity, 
sqequalAxiom
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}].  \mforall{}[i:\mBbbZ{}].    (i\^{}n  \msim{}  i  *  i\^{}n  -  1)
Date html generated:
2017_04_14-AM-09_22_24
Last ObjectModification:
2017_02_27-PM-03_57_44
Theory : int_2
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