Nuprl Lemma : rel_exp1
∀[T:Type]. ∀[R:T ⟶ T ⟶ Type]. ∀[x:T]. ∀y:T. (R^1 x y ⇐⇒ R x y)
Proof
Definitions occuring in Statement :
rel_exp: R^n,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
rel_exp: R^n,
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
infix_ap: x f y,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
rev_implies: P ⇐ Q,
cand: A c∧ B,
guard: {T},
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
istype-universe,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
independent_pairFormation,
sqequalHypSubstitution,
productElimination,
thin,
Error :productIsType,
Error :inhabitedIsType,
hypothesisEquality,
Error :universeIsType,
applyEquality,
Error :equalityIstype,
hypothesis,
Error :dependent_pairFormation_alt,
cut,
because_Cache,
Error :functionIsType,
instantiate,
introduction,
extract_by_obid,
isectElimination,
universeEquality,
hyp_replacement,
equalitySymmetry
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} Type]. \mforall{}[x:T]. \mforall{}y:T. (rel\_exp(T; R; 1) x y \mLeftarrow{}{}\mRightarrow{} R x y)
Date html generated:
2019_06_20-PM-00_30_23
Last ObjectModification:
2019_02_26-AM-11_54_11
Theory : relations
Home
Index