### Nuprl Lemma : rel_plus_minimal

`∀[T:Type]. ∀[R,Q:T ⟶ T ⟶ ℙ].  (R => Q `` Trans(T;x,y.x Q y) `` R+ => Q)`

Proof

Definitions occuring in Statement :  rel_plus: `R+` rel_implies: `R1 => R2` trans: `Trans(T;x,y.E[x; y])` uall: `∀[x:A]. B[x]` prop: `ℙ` infix_ap: `x f y` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` implies: `P `` Q` so_apply: `x[s1;s2]` infix_ap: `x f y` all: `∀x:A. B[x]` prop: `ℙ` rel_implies: `R1 => R2` so_lambda: `λ2x y.t[x; y]` guard: `{T}`
Lemmas referenced :  rel_plus_closure rel_plus_wf trans_wf rel_implies_wf
Rules used in proof :  cut lemma_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation hypothesis sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaFormation independent_functionElimination sqequalRule applyEquality because_Cache lambdaEquality functionEquality cumulativity universeEquality dependent_functionElimination

Latex:
\mforall{}[T:Type].  \mforall{}[R,Q:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (R  =>  Q  {}\mRightarrow{}  Trans(T;x,y.x  Q  y)  {}\mRightarrow{}  R\msupplus{}  =>  Q)

Date html generated: 2016_05_14-PM-03_55_13
Last ObjectModification: 2015_12_26-PM-06_55_43

Theory : relations2

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