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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