Nuprl Lemma : rel_star_weakening

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

Proof

Definitions occuring in Statement :  rel_star: `R^*` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` prop: `ℙ` infix_ap: `x f y` function: `x:A ⟶ B[x]` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` uimplies: `b supposing a` member: `t ∈ T` rel_star: `R^*` infix_ap: `x f y` exists: `∃x:A. B[x]` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` rel_exp: `R^n` ifthenelse: `if b then t else f fi ` eq_int: `(i =z j)` btrue: `tt`
Lemmas referenced :  false_wf le_wf rel_exp_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut introduction axiomEquality hypothesis thin rename sqequalRule dependent_pairFormation dependent_set_memberEquality natural_numberEquality independent_pairFormation lambdaFormation lemma_by_obid sqequalHypSubstitution isectElimination hypothesisEquality applyEquality functionEquality cumulativity universeEquality

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

Date html generated: 2016_05_14-AM-06_04_07
Last ObjectModification: 2015_12_26-AM-11_33_24

Theory : relations

Home Index