Nuprl Lemma : sq_stable__group_p
∀[T:Type]. ∀[op:T ⟶ T ⟶ T]. ∀[id:T]. ∀[inv:T ⟶ T]. SqStable(IsGroup(T;op;id;inv))
Proof
Definitions occuring in Statement :
group_p: IsGroup(T;op;id;inv),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
group_p: IsGroup(T;op;id;inv),
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
implies: P ⇒ Q,
sq_stable: SqStable(P),
and: P ∧ Q,
monoid_p: IsMonoid(T;op;id),
assoc: Assoc(T;op),
ident: Ident(T;op;id),
inverse: Inverse(T;op;id;inv)
Lemmas referenced :
sq_stable__and,
monoid_p_wf,
inverse_wf,
sq_stable__monoid_p,
sq_stable__inverse,
squash_wf,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
isect_memberEquality,
independent_functionElimination,
lambdaFormation,
because_Cache,
lambdaEquality,
dependent_functionElimination,
productElimination,
independent_pairEquality,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[op:T {}\mrightarrow{} T {}\mrightarrow{} T]. \mforall{}[id:T]. \mforall{}[inv:T {}\mrightarrow{} T]. SqStable(IsGroup(T;op;id;inv))
Date html generated:
2016_05_15-PM-00_06_10
Last ObjectModification:
2015_12_26-PM-11_47_39
Theory : groups_1
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