Nuprl Lemma : rng_nexp_zero
∀[r:Rng]. ∀[e:|r|]. ((e ↑r 0) = 1 ∈ |r|)
Proof
Definitions occuring in Statement :
rng_nexp: e ↑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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng_nexp: e ↑r n,
mul_mon_of_rng: r↓xmn,
grp_car: |g|,
pi1: fst(t),
grp_id: e,
pi2: snd(t),
rng: Rng
Lemmas referenced :
mon_nat_op_zero,
mul_mon_of_rng_wf_c,
rng_car_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
isect_memberEquality,
axiomEquality,
setElimination,
rename
Latex:
\mforall{}[r:Rng]. \mforall{}[e:|r|]. ((e \muparrow{}r 0) = 1)
Date html generated:
2016_05_15-PM-00_27_17
Last ObjectModification:
2015_12_26-PM-11_59_00
Theory : rings_1
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