Nuprl Lemma : gamma-neighbourhood_wf
∀[beta:ℕ ⟶ ℕ]. ∀[n0:finite-nat-seq()]. (gamma-neighbourhood(beta;n0) ∈ finite-nat-seq() ⟶ (ℕ?))
Proof
Definitions occuring in Statement :
gamma-neighbourhood: gamma-neighbourhood(beta;n0),
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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
gamma-neighbourhood: gamma-neighbourhood(beta;n0),
all: ∀x:A. B[x],
implies: P ⇒ Q,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
so_apply: x[s],
decidable: Dec(P)
Lemmas referenced :
init-seg-nat-seq_wf,
bool_wf,
eqtt_to_assert,
it_wf,
nat_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
finite-nat-seq_wf,
extend-seq1-all-dec,
all_wf,
decidable_wf,
exists_wf,
assert_wf,
append-finite-nat-seq_wf,
mk-finite-nat-seq_wf,
false_wf,
le_wf,
int_seg_wf,
not_wf,
equal-wf-T-base,
int_seg_subtype_nat,
unit_wf2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
sqequalRule,
inrEquality,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
because_Cache,
voidElimination,
axiomEquality,
isect_memberEquality,
functionEquality,
applyEquality,
productEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
intEquality,
functionExtensionality,
baseClosed,
setElimination,
rename,
inlEquality
Latex:
\mforall{}[beta:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[n0:finite-nat-seq()]. (gamma-neighbourhood(beta;n0) \mmember{} finite-nat-seq() {}\mrightarrow{} (\mBbbN{}?))
Date html generated:
2017_04_20-AM-07_30_26
Last ObjectModification:
2017_02_27-PM-06_00_57
Theory : continuity
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