Nuprl Lemma : rel_star_monotone

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

Proof

Definitions occuring in Statement :  rel_star: `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_star: `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` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  rel_exp_wf exists_wf nat_wf all_wf rel_exp_monotone
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep Error :isect_memberFormation_alt,  lambdaFormation sqequalHypSubstitution productElimination thin dependent_pairFormation hypothesisEquality cut dependent_functionElimination hypothesis independent_functionElimination applyEquality introduction extract_by_obid isectElimination lambdaEquality functionEquality Error :inhabitedIsType,  Error :functionIsType,  Error :universeIsType,  universeEquality

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

Date html generated: 2019_06_20-PM-00_30_34
Last ObjectModification: 2018_09_26-PM-00_49_26

Theory : relations

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