### Nuprl Lemma : action_p_wf

`∀[A:Type]. ∀[x:A ⟶ A ⟶ A]. ∀[e:A]. ∀[S:Type]. ∀[f:A ⟶ S ⟶ S].  (IsAction(A;x;e;S;f) ∈ ℙ)`

Proof

Definitions occuring in Statement :  action_p: `IsAction(A;x;e;S;f)` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  action_p: `IsAction(A;x;e;S;f)` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` infix_ap: `x f y` so_apply: `x[s]`
Lemmas referenced :  and_wf uall_wf all_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry functionEquality isect_memberEquality because_Cache universeEquality

Latex:
\mforall{}[A:Type].  \mforall{}[x:A  {}\mrightarrow{}  A  {}\mrightarrow{}  A].  \mforall{}[e:A].  \mforall{}[S:Type].  \mforall{}[f:A  {}\mrightarrow{}  S  {}\mrightarrow{}  S].    (IsAction(A;x;e;S;f)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_15-PM-00_02_33
Last ObjectModification: 2015_12_26-PM-11_26_00

Theory : gen_algebra_1

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