Nuprl Lemma : int-to-ring_wf
∀[r:Rng]. ∀[n:ℤ]. (int-to-ring(r;n) ∈ |r|)
Proof
Definitions occuring in Statement :
int-to-ring: int-to-ring(r;n),
rng: Rng,
rng_car: |r|,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int-to-ring: int-to-ring(r;n),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
rng: Rng,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
bfalse: ff,
guard: {T}
Lemmas referenced :
lt_int_wf,
bool_wf,
uiff_transitivity,
equal-wf-base,
int_subtype_base,
assert_wf,
less_than_wf,
eqtt_to_assert,
assert_of_lt_int,
rng_minus_wf,
rng_nat_op_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermMinus_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_minus_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
rng_one_wf,
le_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
equal_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
independent_functionElimination,
because_Cache,
productElimination,
independent_isectElimination,
setElimination,
rename,
dependent_set_memberEquality,
dependent_functionElimination,
minusEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
equalityTransitivity,
equalitySymmetry,
axiomEquality
Latex:
\mforall{}[r:Rng]. \mforall{}[n:\mBbbZ{}]. (int-to-ring(r;n) \mmember{} |r|)
Date html generated:
2017_10_01-AM-08_18_55
Last ObjectModification:
2017_02_28-PM-02_03_43
Theory : rings_1
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