Nuprl Lemma : monoid_p_wf
∀[T:Type]. ∀[op:T ⟶ T ⟶ T]. ∀[id:T]. (IsMonoid(T;op;id) ∈ ℙ)
Proof
Definitions occuring in Statement :
monoid_p: IsMonoid(T;op;id),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
monoid_p: IsMonoid(T;op;id),
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
and_wf,
assoc_wf,
ident_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{}[op:T {}\mrightarrow{} T {}\mrightarrow{} T]. \mforall{}[id:T]. (IsMonoid(T;op;id) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_06_06
Last ObjectModification:
2015_12_26-PM-11_47_32
Theory : groups_1
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