Nuprl Lemma : rec-comb_wf
∀[Info:Type]. ∀[n:ℕ]. ∀[A:ℕn ⟶ Type]. ∀[X:i:ℕn ⟶ EClass(A i)]. ∀[T:Type]. ∀[f:Id
⟶ (i:ℕn ⟶ bag(A i))
⟶ bag(T)
⟶ bag(T)]. ∀[init:Id ⟶ bag(T)].
(rec-comb(X;f;init) ∈ EClass(T))
Proof
Definitions occuring in Statement :
rec-comb: rec-comb(X;f;init),
eclass: EClass(A[eo; e]),
Id: Id,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eclass: EClass(A[eo; e]),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
rec-comb: rec-comb(X;f;init),
primed-class-opt: Prior(X)?b,
sq_exists: ∃x:{A| B[x]},
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[Info:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[X:i:\mBbbN{}n {}\mrightarrow{} EClass(A i)]. \mforall{}[T:Type]. \mforall{}[f:Id
{}\mrightarrow{} (i:\mBbbN{}n
{}\mrightarrow{} bag(A i))
{}\mrightarrow{} bag(T)
{}\mrightarrow{} bag(T)].
\mforall{}[init:Id {}\mrightarrow{} bag(T)].
(rec-comb(X;f;init) \mmember{} EClass(T))
Date html generated:
2016_05_17-AM-00_00_23
Last ObjectModification:
2016_01_17-PM-07_03_13
Theory : event-ordering
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