Nuprl Lemma : min-increasing-sequence_wf
∀[a:ℕ ⟶ ℕ]. ∀[n,k:ℕ]. (min-increasing-sequence(a;n;k) ∈ ℕ?)
Proof
Definitions occuring in Statement :
min-increasing-sequence: min-increasing-sequence(a;n;k),
nat: ℕ,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right
Definitions unfolded in proof :
assert: ↑b,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
or: P ∨ Q,
exists: ∃x:A. B[x],
bfalse: ff,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
exposed-bfalse: exposed-bfalse,
all: ∀x:A. B[x],
prop: ℙ,
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
nat: ℕ,
min-increasing-sequence: min-increasing-sequence(a;n;k),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
int_seg_wf,
le_wf,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
assert_of_le_int,
eqtt_to_assert,
bool_wf,
false_wf,
int_seg_subtype_nat,
le_int_wf,
it_wf,
unit_wf2,
nat_wf,
primrec_wf
Rules used in proof :
functionEquality,
isect_memberEquality,
axiomEquality,
voidElimination,
independent_functionElimination,
cumulativity,
instantiate,
dependent_functionElimination,
promote_hyp,
dependent_pairFormation,
equalitySymmetry,
equalityTransitivity,
productElimination,
equalityElimination,
lambdaFormation,
independent_pairFormation,
independent_isectElimination,
natural_numberEquality,
functionExtensionality,
applyEquality,
rename,
setElimination,
inlEquality,
unionElimination,
lambdaEquality,
because_Cache,
inrEquality,
hypothesisEquality,
hypothesis,
unionEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[n,k:\mBbbN{}]. (min-increasing-sequence(a;n;k) \mmember{} \mBbbN{}?)
Date html generated:
2017_04_20-AM-07_36_47
Last ObjectModification:
2017_04_18-AM-10_34_37
Theory : continuity
Home
Index