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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