Nuprl Lemma : altneg-altneg
∀[T:Type]. ∀[X:n:ℕ ⟶ (ℕn ⟶ T) ⟶ 𝔹]. (¬(¬(X)) = X ∈ (n:ℕ ⟶ (ℕn ⟶ T) ⟶ 𝔹))
Proof
Definitions occuring in Statement :
altneg: ¬(A),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
nat: ℕ,
altneg: ¬(A),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
bool_wf,
istype-nat,
nat_wf,
int_seg_wf,
bnot_bnot_elim
Rules used in proof :
universeEquality,
instantiate,
Error :inhabitedIsType,
Error :isectIsTypeImplies,
axiomEquality,
Error :isect_memberEquality_alt,
Error :universeIsType,
Error :functionIsType,
rename,
setElimination,
natural_numberEquality,
functionEquality,
hypothesis,
hypothesisEquality,
applyEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
functionExtensionality,
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{}]. (\mneg{}(\mneg{}(X)) = X)
Date html generated:
2019_06_20-PM-02_46_20
Last ObjectModification:
2019_06_06-PM-02_00_10
Theory : fan-theorem
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