Nuprl Lemma : b-exists_wf
∀[n:ℕ]. ∀[P:ℕn ⟶ 𝔹]. ((∃i<n.P[i])_b ∈ 𝔹)
Proof
Definitions occuring in Statement :
b-exists: (∃i<n.P[i])_b,
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
b-exists: (∃i<n.P[i])_b,
so_apply: x[s],
nat: ℕ
Lemmas referenced :
primrec_wf,
bool_wf,
bfalse_wf,
bor_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
lambdaEquality,
applyEquality,
natural_numberEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[P:\mBbbN{}n {}\mrightarrow{} \mBbbB{}]. ((\mexists{}i<n.P[i])\_b \mmember{} \mBbbB{})
Date html generated:
2016_05_13-PM-04_00_37
Last ObjectModification:
2015_12_26-AM-10_49_31
Theory : bool_1
Home
Index