Nuprl Lemma : rel_rel_star
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀x,y:T. ((x R y) ⇒ (x (R^*) y))
Proof
Definitions occuring in Statement :
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 :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
infix_ap: x f y,
rel_star: R^*,
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
rel_exp: R^n,
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt
Lemmas referenced :
false_wf,
le_wf,
rel_exp_wf,
and_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
applyEquality,
hypothesisEquality,
functionEquality,
cumulativity,
universeEquality,
sqequalRule,
dependent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
hypothesis,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}x,y:T. ((x R y) {}\mRightarrow{} (x rel\_star(T; R) y))
Date html generated:
2016_05_14-AM-06_04_04
Last ObjectModification:
2015_12_26-AM-11_33_28
Theory : relations
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