Nuprl Lemma : rel_path_wf
∀[A:Type]. ∀[R:A ⟶ A ⟶ ℙ]. ∀[x,y:A]. ∀[L:(a:A × b:A × (R a b)) List]. (rel_path(A;L;x;y) ∈ ℙ)
Proof
Definitions occuring in Statement :
rel_path: rel_path(A;L;x;y),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rel_path: rel_path(A;L;x;y),
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
and: P ∧ Q,
pi1: fst(t),
pi2: snd(t),
so_apply: x[s1;s2;s3]
Lemmas referenced :
list_ind_wf,
equal_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
productEquality,
cumulativity,
hypothesisEquality,
because_Cache,
functionExtensionality,
hypothesis,
lambdaEquality,
functionEquality,
universeEquality,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. \mforall{}[x,y:A]. \mforall{}[L:(a:A \mtimes{} b:A \mtimes{} (R a b)) List]. (rel\_path(A;L;x;y) \mmember{} \mBbbP{})
Date html generated:
2017_04_17-AM-09_25_35
Last ObjectModification:
2017_02_27-PM-05_26_14
Theory : relations2
Home
Index