### Nuprl Lemma : rel_plus_functionality_wrt_rel_implies

`∀[T:Type]. ∀[R1,R2:T ⟶ T ⟶ ℙ].  (R1 => R2 `` R1+ => R2+)`

Proof

Definitions occuring in Statement :  rel_plus: `R+` rel_implies: `R1 => R2` uall: `∀[x:A]. B[x]` prop: `ℙ` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  rel_plus: `R+` rel_implies: `R1 => R2` infix_ap: `x f y` uall: `∀[x:A]. B[x]` implies: `P `` Q` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` member: `t ∈ T` prop: `ℙ` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  rel_exp_wf exists_wf nat_plus_wf nat_plus_subtype_nat all_wf rel_exp_monotone
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation sqequalHypSubstitution productElimination thin dependent_pairFormation hypothesisEquality cut dependent_functionElimination hypothesis independent_functionElimination applyEquality lemma_by_obid isectElimination because_Cache lambdaEquality functionEquality cumulativity universeEquality

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

Date html generated: 2016_05_14-PM-03_54_01
Last ObjectModification: 2015_12_26-PM-06_56_15

Theory : relations2

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