Nuprl Lemma : subsequence_wf
∀[T:Type]. ∀[E:T ⟶ T ⟶ ℙ]. ∀[x,y:ℕ ⟶ T].  (subsequence(a,b.E[a;b];n.x[n];n.y[n]) ∈ ℙ)
Proof
Definitions occuring in Statement : 
subsequence: subsequence(a,b.E[a; b];m.x[m];n.y[n])
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
so_apply: x[s1;s2]
, 
so_apply: x[s]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
subsequence: subsequence(a,b.E[a; b];m.x[m];n.y[n])
, 
prop: ℙ
, 
exists: ∃x:A. B[x]
, 
all: ∀x:A. B[x]
, 
uimplies: b supposing a
, 
nat: ℕ
, 
and: P ∧ Q
, 
so_apply: x[s1;s2]
, 
so_apply: x[s]
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
nat_wf, 
le_wf, 
subtype_rel_self, 
istype-nat, 
istype-universe
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
productEquality, 
extract_by_obid, 
hypothesis, 
functionEquality, 
isectEquality, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
setElimination, 
rename, 
hypothesisEquality, 
because_Cache, 
applyEquality, 
instantiate, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
Error :inhabitedIsType, 
Error :isect_memberEquality_alt, 
Error :isectIsTypeImplies, 
Error :functionIsType, 
Error :universeIsType, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[E:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[x,y:\mBbbN{}  {}\mrightarrow{}  T].    (subsequence(a,b.E[a;b];n.x[n];n.y[n])  \mmember{}  \mBbbP{})
Date html generated:
2019_06_20-PM-00_31_48
Last ObjectModification:
2019_04_22-PM-01_48_04
Theory : relations
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