Nuprl Lemma : bsc-body_wf
∀[T:Type]. ∀[F:(ℕ ⟶ T) ⟶ ℕ]. ∀[M:n:ℕ ⟶ (ℕn ⟶ T) ⟶ (ℕ ⋃ (ℕ × ℕ))]. ∀[f:ℕ ⟶ T]. (bsc-body(F;M;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
bsc-body: bsc-body(F;M;f),
int_seg: {i..j-},
nat: ℕ,
b-union: A ⋃ B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bsc-body: bsc-body(F;M;f),
prop: ℙ,
and: P ∧ Q,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
uimplies: b supposing a,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x],
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
pi2: snd(t),
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
nat_wf,
subtype_rel_function,
int_seg_wf,
int_seg_subtype_nat,
istype-false,
subtype_rel_self,
equal-wf-base,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
product_subtype_base,
isect_wf,
true_wf,
false_wf,
equal_wf,
istype-universe,
all_wf,
istype-nat,
b-union_wf,
istype-void,
subtype_base_sq,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
hypothesis,
applyEquality,
hypothesisEquality,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
because_Cache,
independent_isectElimination,
independent_pairFormation,
Error :lambdaFormation_alt,
Error :inhabitedIsType,
imageElimination,
productElimination,
unionElimination,
equalityElimination,
intEquality,
Error :lambdaEquality_alt,
Error :equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
functionEquality,
isintReduceTrue,
axiomEquality,
Error :functionIsType,
Error :universeIsType,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
instantiate,
universeEquality,
voidElimination,
cumulativity
Latex:
\mforall{}[T:Type]. \mforall{}[F:(\mBbbN{} {}\mrightarrow{} T) {}\mrightarrow{} \mBbbN{}]. \mforall{}[M:n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} T) {}\mrightarrow{} (\mBbbN{} \mcup{} (\mBbbN{} \mtimes{} \mBbbN{}))]. \mforall{}[f:\mBbbN{} {}\mrightarrow{} T].
(bsc-body(F;M;f) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_50_08
Last ObjectModification:
2019_02_11-AM-11_17_31
Theory : continuity
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