Nuprl Lemma : exp_functionality_wrt_assoced
∀n:ℕ. ∀x,y:ℤ. ((x ~ y) ⇒ (x^n ~ y^n))
Proof
Definitions occuring in Statement :
assoced: a ~ b,
exp: i^n,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
and: P ∧ Q,
so_apply: x[s],
exp: i^n,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
multiply_functionality_wrt_assoced,
assoced_functionality_wrt_assoced,
primrec-unroll,
assert_of_bnot,
eqff_to_assert,
iff_weakening_uiff,
not_wf,
bnot_wf,
bfalse_wf,
iff_transitivity,
int_formula_prop_eq_lemma,
intformeq_wf,
assert_of_eq_int,
eqtt_to_assert,
assert_wf,
btrue_wf,
equal_wf,
uiff_transitivity,
bool_wf,
eq_int_wf,
assoced_weakening,
exp0_lemma,
nat_wf,
primrec-wf2,
less_than_wf,
set_wf,
le_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
subtract_wf,
decidable__le,
exp_wf2,
assoced_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
rename,
setElimination,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
intEquality,
sqequalRule,
lambdaEquality,
because_Cache,
functionEquality,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
introduction,
equalityElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
impliesFunctionality,
equalityEquality,
multiplyEquality
Latex:
\mforall{}n:\mBbbN{}. \mforall{}x,y:\mBbbZ{}. ((x \msim{} y) {}\mRightarrow{} (x\^{}n \msim{} y\^{}n))
Date html generated:
2016_05_15-PM-04_50_56
Last ObjectModification:
2016_01_16-AM-11_26_53
Theory : general
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