Nuprl Lemma : tree-big_wf
∀[T:Type]. ∀[A:(T List) ⟶ ℙ]. ∀[n:ℕ]. (tree-big(T;A;n) ∈ ℙ)
Proof
Definitions occuring in Statement :
tree-big: tree-big(T;A;n),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
tree-big: tree-big(T;A;n),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
all_wf,
list_wf,
equal_wf,
length_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
intEquality,
setElimination,
rename,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[A:(T List) {}\mrightarrow{} \mBbbP{}]. \mforall{}[n:\mBbbN{}]. (tree-big(T;A;n) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-04_10_06
Last ObjectModification:
2015_12_26-PM-07_54_24
Theory : fan-theorem
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