### Nuprl Lemma : fun-equiv_wf

`∀[X,A:Type]. ∀[E:A ⟶ A ⟶ ℙ]. ∀[f,g:X ⟶ A].  (fun-equiv(X;a,b.E[a;b];f;g) ∈ ℙ)`

Proof

Definitions occuring in Statement :  fun-equiv: `fun-equiv(X;a,b.E[a; b];f;g)` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s1;s2]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` fun-equiv: `fun-equiv(X;a,b.E[a; b];f;g)` so_lambda: `λ2x.t[x]` so_apply: `x[s1;s2]` so_apply: `x[s]` prop: `ℙ`
Lemmas referenced :  all_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry functionEquality isect_memberEquality because_Cache cumulativity universeEquality

Latex:
\mforall{}[X,A:Type].  \mforall{}[E:A  {}\mrightarrow{}  A  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[f,g:X  {}\mrightarrow{}  A].    (fun-equiv(X;a,b.E[a;b];f;g)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_14-AM-06_09_08
Last ObjectModification: 2015_12_26-AM-11_48_12

Theory : quot_1

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