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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