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
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