### Nuprl Lemma : detach_fun_wf

`∀[T:Type]. ∀[A:T ⟶ ℙ].  (detach_fun(T;A) ∈ Type)`

Proof

Definitions occuring in Statement :  detach_fun: `detach_fun(T;A)` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  detach_fun: `detach_fun(T;A)` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` so_apply: `x[s]` iff: `P `⇐⇒` Q` all: `∀x:A. B[x]` rev_implies: `P `` Q` implies: `P `` Q` and: `P ∧ Q` prop: `ℙ`
Lemmas referenced :  bool_wf all_wf iff_wf assert_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut setEquality functionEquality hypothesisEquality lemma_by_obid hypothesis sqequalHypSubstitution isectElimination thin lambdaEquality applyEquality axiomEquality equalityTransitivity equalitySymmetry cumulativity universeEquality isect_memberEquality because_Cache

Latex:
\mforall{}[T:Type].  \mforall{}[A:T  {}\mrightarrow{}  \mBbbP{}].    (detach\_fun(T;A)  \mmember{}  Type)

Date html generated: 2016_05_15-PM-00_00_22
Last ObjectModification: 2015_12_26-PM-11_26_51

Theory : gen_algebra_1

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