Nuprl Lemma : int-to-ring-zero
∀[r:Top]. (int-to-ring(r;0) ~ 0)
Proof
Definitions occuring in Statement :
int-to-ring: int-to-ring(r;n),
rng_zero: 0,
uall: ∀[x:A]. B[x],
top: Top,
natural_number: $n,
sqequal: s ~ 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,
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalAxiom,
lemma_by_obid,
hypothesis
Latex:
\mforall{}[r:Top]. (int-to-ring(r;0) \msim{} 0)
Date html generated:
2016_05_15-PM-00_27_05
Last ObjectModification:
2015_12_26-PM-11_59_09
Theory : rings_1
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