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,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
so_apply: x[s],
exp: i^n,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
all_wf,
assoced_wf,
exp_wf2,
decidable__le,
subtract_wf,
full-omega-unsat,
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,
set_wf,
less_than_wf,
primrec-wf2,
nat_wf,
exp0_lemma,
assoced_weakening,
lt_int_wf,
bool_wf,
uiff_transitivity,
equal-wf-base,
int_subtype_base,
assert_wf,
eqtt_to_assert,
assert_of_lt_int,
le_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
equal_wf,
primrec-unroll,
assoced_functionality_wrt_assoced,
multiply_functionality_wrt_assoced
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
rename,
setElimination,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
intEquality,
sqequalRule,
lambdaEquality,
because_Cache,
functionEquality,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
equalityElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
multiplyEquality
Latex:
\mforall{}n:\mBbbN{}. \mforall{}x,y:\mBbbZ{}. ((x \msim{} y) {}\mRightarrow{} (x\^{}n \msim{} y\^{}n))
Date html generated:
2018_05_21-PM-01_10_37
Last ObjectModification:
2018_05_19-AM-06_39_30
Theory : num_thy_1
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