### Nuprl Lemma : strict-fun-connected_transitivity2

[T:Type]. ∀f:T ⟶ T. (retraction(T;f)  (∀x,y,z:T.  (y is f*(x)  f+(y)  f+(x))))

Proof

Definitions occuring in Statement :  retraction: retraction(T;f) strict-fun-connected: f+(x) fun-connected: is f*(x) uall: [x:A]. B[x] all: x:A. B[x] implies:  Q function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  strict-fun-connected: f+(x) uall: [x:A]. B[x] all: x:A. B[x] implies:  Q and: P ∧ Q cand: c∧ B member: t ∈ T guard: {T} prop: not: ¬A false: False uimplies: supposing a
Lemmas referenced :  fun-connected_transitivity not_wf equal_wf fun-connected_wf retraction_wf fun-connected_antisymmetry
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation sqequalHypSubstitution productElimination thin cut independent_pairFormation hypothesis introduction extract_by_obid isectElimination hypothesisEquality dependent_functionElimination independent_functionElimination productEquality cumulativity functionExtensionality applyEquality functionEquality universeEquality equalitySymmetry hyp_replacement Error :applyLambdaEquality,  voidElimination independent_isectElimination equalityTransitivity

Latex:
\mforall{}[T:Type].  \mforall{}f:T  {}\mrightarrow{}  T.  (retraction(T;f)  {}\mRightarrow{}  (\mforall{}x,y,z:T.    (y  is  f*(x)  {}\mRightarrow{}  z  =  f+(y)  {}\mRightarrow{}  z  =  f+(x))))

Date html generated: 2016_10_25-AM-11_04_15
Last ObjectModification: 2016_07_12-AM-07_12_20

Theory : general

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