Nuprl Lemma : rng_nat_op_wf
∀[r:Rng]. ∀[n:ℕ]. ∀[u:|r|]. (n ⋅r u ∈ |r|)
Proof
Definitions occuring in Statement :
rng_nat_op: n ⋅r e,
rng: Rng,
rng_car: |r|,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
rng_nat_op: n ⋅r e,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
add_grp_of_rng: r↓+gp,
grp_car: |g|,
pi1: fst(t),
rng: Rng
Lemmas referenced :
mon_nat_op_wf2,
add_grp_of_rng_wf_a,
nat_subtype,
rng_car_wf,
nat_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
setElimination,
rename,
isect_memberEquality
Latex:
\mforall{}[r:Rng]. \mforall{}[n:\mBbbN{}]. \mforall{}[u:|r|]. (n \mcdot{}r u \mmember{} |r|)
Date html generated:
2016_05_15-PM-00_26_46
Last ObjectModification:
2015_12_26-PM-11_59_34
Theory : rings_1
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