Nuprl Lemma : fun-connected_wf

[T:Type]. ∀[f:T ⟶ T]. ∀[x,y:T].  (y is f*(x) ∈ ℙ)


Proof




Definitions occuring in Statement :  fun-connected: is f*(x) uall: [x:A]. B[x] prop: member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  fun-connected: is f*(x) uall: [x:A]. B[x] member: t ∈ T so_lambda: λ2x.t[x] so_apply: x[s]
Lemmas referenced :  exists_wf list_wf fun-path_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis lambdaEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache functionEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[f:T  {}\mrightarrow{}  T].  \mforall{}[x,y:T].    (y  is  f*(x)  \mmember{}  \mBbbP{})



Date html generated: 2016_05_15-PM-04_58_01
Last ObjectModification: 2015_12_27-PM-02_30_08

Theory : general


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