Nuprl Lemma : ring_p_wf
∀[T:Type]. ∀[pl:T ⟶ T ⟶ T]. ∀[zero:T]. ∀[neg:T ⟶ T]. ∀[tm:T ⟶ T ⟶ T]. ∀[one:T]. (IsRing(T;pl;zero;neg;tm;one) ∈ ℙ)
Proof
Definitions occuring in Statement :
ring_p: IsRing(T;plus;zero;neg;times;one),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
ring_p: IsRing(T;plus;zero;neg;times;one),
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
and_wf,
group_p_wf,
monoid_p_wf,
bilinear_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[pl:T {}\mrightarrow{} T {}\mrightarrow{} T]. \mforall{}[zero:T]. \mforall{}[neg:T {}\mrightarrow{} T]. \mforall{}[tm:T {}\mrightarrow{} T {}\mrightarrow{} T]. \mforall{}[one:T].
(IsRing(T;pl;zero;neg;tm;one) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_20_21
Last ObjectModification:
2015_12_27-AM-00_02_58
Theory : rings_1
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