Nuprl Lemma : neighbourhood-function-nat_wf
∀[G:finite-nat-seq() ⟶ (ℕ?)]. (K0(G) ∈ Type)
Proof
Definitions occuring in Statement :
neighbourhood-function-nat: K0(G),
finite-nat-seq: finite-nat-seq(),
nat: ℕ,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
neighbourhood-function-nat: K0(G),
and: P ∧ Q,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
nat: ℕ,
uimplies: b supposing a,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x]
Lemmas referenced :
all_wf,
nat_wf,
exists_wf,
assert_wf,
isl_wf,
unit_wf2,
finite-nat-seq_wf,
mk-finite-nat-seq_wf,
subtype_rel_dep_function,
int_seg_wf,
int_seg_subtype_nat,
false_wf,
subtype_rel_self,
equal_wf,
append-finite-nat-seq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
because_Cache,
lambdaEquality,
applyEquality,
functionExtensionality,
hypothesisEquality,
natural_numberEquality,
setElimination,
rename,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
unionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[G:finite-nat-seq() {}\mrightarrow{} (\mBbbN{}?)]. (K0(G) \mmember{} Type)
Date html generated:
2017_04_20-AM-07_29_06
Last ObjectModification:
2017_02_27-PM-05_59_37
Theory : continuity
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