Nuprl Lemma : int_mod_ring_wf
∀[n:ℕ+]. (int_mod_ring(n) ∈ CDRng)
Proof
Definitions occuring in Statement :
int_mod_ring: int_mod_ring(n),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
cdrng: CDRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_mod_ring: int_mod_ring(n),
cdrng: CDRng,
rng_car: |r|,
pi1: fst(t),
rng_eq: =b,
pi2: snd(t),
crng: CRng,
rng_times: *,
rng: Rng,
rng_plus: +r,
rng_zero: 0,
rng_minus: -r,
rng_one: 1,
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
rng_sig: RngSig,
ring_p: IsRing(T;plus;zero;neg;times;one),
bilinear: BiLinear(T;pl;tm),
monoid_p: IsMonoid(T;op;id),
group_p: IsGroup(T;op;id;inv),
infix_ap: x f y,
ident: Ident(T;op;id),
assoc: Assoc(T;op),
inverse: Inverse(T;op;id;inv),
and: P ∧ Q,
cand: A c∧ B,
squash: ↓T,
prop: ℙ,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
comm: Comm(T;op),
uiff: uiff(P;Q),
eqfun_p: IsEqFun(T;eq),
int_seg: {i..j-}
Lemmas referenced :
nat_plus_wf,
bool_wf,
unit_wf2,
add_wf_int_mod,
bfalse_wf,
modulus_wf_int_mod,
eq_int_wf,
int_mod_wf,
minus_wf_int_mod,
it_wf,
int-subtype-int_mod,
multiply_wf_int_mod,
add_assoc_int_mod,
add_zero_int_mod,
add-commutes,
add_inverse_int_mod,
multiply_assoc_int_mod,
multiply_one_int_mod,
mul-commutes,
multiply_distrib_int_mod,
multiply_distrib2_int_mod,
equal_wf,
squash_wf,
true_wf,
istype-universe,
add_com_int_mod,
subtype_rel_self,
iff_weakening_equal,
rng_one_wf,
rng_times_wf,
rng_minus_wf,
rng_zero_wf,
rng_plus_wf,
rng_car_wf,
ring_p_wf,
multiply_com_int_mod,
comm_wf,
assert_witness,
assert_of_eq_int,
assert_wf,
iff_weakening_uiff,
equal_int_mod_iff_modulus,
int_subtype_base,
rng_eq_wf,
eqfun_p_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
extract_by_obid,
dependent_set_memberEquality_alt,
unionEquality,
functionEquality,
productEquality,
unionIsType,
functionIsType,
productIsType,
natural_numberEquality,
closedConclusion,
inhabitedIsType,
because_Cache,
applyEquality,
lambdaEquality_alt,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
dependent_pairEquality_alt,
inrEquality_alt,
isect_memberEquality_alt,
isectIsTypeImplies,
independent_pairFormation,
Error :memTop,
productElimination,
independent_pairEquality,
imageElimination,
instantiate,
universeEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination,
isect_memberEquality,
isect_memberFormation,
equalityIsType1,
promote_hyp,
intEquality,
equalityIsType4
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. (int\_mod\_ring(n) \mmember{} CDRng)
Date html generated:
2020_05_20-AM-08_20_46
Last ObjectModification:
2019_12_31-PM-06_31_25
Theory : general
Home
Index