Nuprl Lemma : int-to-ring-one
∀[r:Rng]. (int-to-ring(r;1) = 1 ∈ |r|)
Proof
Definitions occuring in Statement :
int-to-ring: int-to-ring(r;n),
rng: Rng,
rng_one: 1,
rng_car: |r|,
uall: ∀[x:A]. B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
int-to-ring: int-to-ring(r;n),
lt_int: i <z j,
ifthenelse: if b then t else f fi ,
bfalse: ff,
rng_nat_op: n ⋅r e,
mon_nat_op: n ⋅ e,
add_grp_of_rng: r↓+gp,
grp_op: *,
pi2: snd(t),
pi1: fst(t),
grp_id: e,
nat_op: n x(op;id) e,
itop: Π(op,id) lb ≤ i < ub. E[i],
ycomb: Y,
subtract: n - m,
btrue: tt,
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng: Rng,
and: P ∧ Q
Lemmas referenced :
rng_plus_zero,
rng_one_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
hypothesis,
productElimination
Latex:
\mforall{}[r:Rng]. (int-to-ring(r;1) = 1)
Date html generated:
2018_05_21-PM-03_14_44
Last ObjectModification:
2018_05_19-AM-08_07_54
Theory : rings_1
Home
Index