Nuprl Lemma : altunbounded_wf
∀[T:Type]. ∀[X:n:ℕ ⟶ (ℕn ⟶ T) ⟶ 𝔹]. (Unbounded(X) ∈ ℙ)
Proof
Definitions occuring in Statement :
altunbounded: Unbounded(A),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
nat: ℕ,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
prop: ℙ,
altunbounded: Unbounded(A),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
bool_wf,
istype-nat,
assert_wf,
int_seg_wf,
nat_wf
Rules used in proof :
universeEquality,
instantiate,
Error :inhabitedIsType,
Error :isectIsTypeImplies,
Error :isect_memberEquality_alt,
Error :universeIsType,
Error :functionIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
hypothesisEquality,
rename,
setElimination,
natural_numberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
productEquality,
hypothesis,
extract_by_obid,
functionEquality,
sqequalRule,
cut,
introduction,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[X:n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} T) {}\mrightarrow{} \mBbbB{}]. (Unbounded(X) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_46_06
Last ObjectModification:
2019_06_06-PM-01_25_11
Theory : fan-theorem
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