Nuprl Lemma : rel-rel-plus
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀x,y:T. ((x R y) ⇒ (x R+ y))
Proof
Definitions occuring in Statement :
rel_plus: 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,
rel_plus: R+,
infix_ap: x f y,
member: t ∈ T,
prop: ℙ,
exists: ∃x:A. B[x],
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
nat_plus_subtype_nat,
rel_exp_wf,
rel_exp_one,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalRule,
applyEquality,
hypothesisEquality,
functionEquality,
cumulativity,
universeEquality,
dependent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
cut,
independent_pairFormation,
introduction,
imageMemberEquality,
thin,
baseClosed,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
isectElimination,
dependent_functionElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}x,y:T. ((x R y) {}\mRightarrow{} (x R\msupplus{} y))
Date html generated:
2016_05_14-PM-03_53_32
Last ObjectModification:
2016_01_14-PM-11_10_37
Theory : relations2
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