Nuprl Lemma : group_p_wf

`∀[T:Type]. ∀[op:T ⟶ T ⟶ T]. ∀[id:T]. ∀[inv:T ⟶ T].  (IsGroup(T;op;id;inv) ∈ ℙ)`

Proof

Definitions occuring in Statement :  group_p: `IsGroup(T;op;id;inv)` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` 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`
Lemmas referenced :  and_wf monoid_p_wf inverse_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 functionEquality isect_memberEquality because_Cache universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[op:T  {}\mrightarrow{}  T  {}\mrightarrow{}  T].  \mforall{}[id:T].  \mforall{}[inv:T  {}\mrightarrow{}  T].    (IsGroup(T;op;id;inv)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_15-PM-00_06_09
Last ObjectModification: 2015_12_26-PM-11_47_37

Theory : groups_1

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