Nuprl Lemma : int-to-ring-hom
∀[r:Rng]. rng_hom_p(ℤ-rng;r;λx.int-to-ring(r;x))
Proof
Definitions occuring in Statement :
int-to-ring: int-to-ring(r;n),
int_ring: ℤ-rng,
rng_hom_p: rng_hom_p(r;s;f),
rng: Rng,
uall: ∀[x:A]. B[x],
lambda: λx.A[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng_hom_p: rng_hom_p(r;s;f),
and: P ∧ Q,
int_ring: ℤ-rng,
rng_car: |r|,
pi1: fst(t),
rng_plus: +r,
pi2: snd(t),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
infix_ap: x f y,
squash: ↓T,
rng: Rng,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
rng_times: *,
rng_one: 1,
cand: A c∧ B,
prop: ℙ,
integ_dom: IntegDom{i},
crng: CRng
Lemmas referenced :
equal_wf,
rng_car_wf,
int-to-ring-add,
infix_ap_wf,
rng_plus_wf,
int-to-ring_wf,
iff_weakening_equal,
int-to-ring-mul,
rng_times_wf,
squash_wf,
true_wf,
int-to-ring-one,
rng_one_wf,
int_ring_wf,
integ_dom_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalRule,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
because_Cache,
hypothesis,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination,
independent_functionElimination,
intEquality,
isect_memberEquality,
axiomEquality,
universeEquality,
independent_pairEquality
Latex:
\mforall{}[r:Rng]. rng\_hom\_p(\mBbbZ{}-rng;r;\mlambda{}x.int-to-ring(r;x))
Date html generated:
2017_10_01-AM-08_19_24
Last ObjectModification:
2017_02_28-PM-02_04_04
Theory : rings_1
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