### Nuprl Lemma : rel_star_monotonic

`∀[T:Type]. ∀[R1,R2:T ⟶ T ⟶ ℙ].  ∀x,y:T.  (R1 => R2 `` (x (R1^*) y) `` (x (R2^*) y))`

Proof

Definitions occuring in Statement :  rel_star: `R^*` rel_implies: `R1 => R2` uall: `∀[x:A]. B[x]` prop: `ℙ` infix_ap: `x f y` all: `∀x:A. B[x]` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` rel_implies: `R1 => R2` prop: `ℙ` infix_ap: `x f y`
Lemmas referenced :  rel_star_monotone rel_star_wf rel_implies_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin because_Cache hypothesisEquality independent_functionElimination hypothesis dependent_functionElimination applyEquality Error :inhabitedIsType,  Error :functionIsType,  Error :universeIsType,  universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[R1,R2:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].
\mforall{}x,y:T.    (R1  =>  R2  {}\mRightarrow{}  (x  (R1\^{}*)  y)  {}\mRightarrow{}  (x  (R2\^{}*)  y))

Date html generated: 2019_06_20-PM-00_30_41
Last ObjectModification: 2018_09_26-PM-00_48_04

Theory : relations

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