### Nuprl Lemma : rel-plus-rel-star

`∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  ∀x,y:T.  ((x R+ y) `` (x (R^*) y))`

Proof

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

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    \mforall{}x,y:T.    ((x  R\msupplus{}  y)  {}\mRightarrow{}  (x  rel\_star(T;  R)  y))

Date html generated: 2016_05_14-PM-03_53_41
Last ObjectModification: 2015_12_26-PM-06_56_35

Theory : relations2

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