Nuprl Lemma : rec-bind-class_wf
∀[Info,A,B:Type]. ∀[X:A ⟶ EClass(B)]. ∀[Y:A ⟶ EClass(A)].
rec-bind-class(X;Y) ∈ A ⟶ EClass(B) supposing not-self-starting{i:l}(Info;A;Y)
Proof
Definitions occuring in Statement :
rec-bind-class: rec-bind-class(X;Y),
not-self-starting: not-self-starting{i:l}(Info;A;Y),
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not-self-starting: not-self-starting{i:l}(Info;A;Y),
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
less_than': less_than'(a;b),
guard: {T},
uiff: uiff(P;Q),
eclass: EClass(A[eo; e]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
rec-bind-class: rec-bind-class(X;Y),
mbind-class: X >>= Y,
parallel-class: X || Y,
bind-class: X >x> Y[x],
eclass-compose2: eclass-compose2(f;X;Y),
so_lambda: λ2x.t[x],
classrel: v ∈ X(e),
so_apply: x[s],
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
sq_stable: SqStable(P),
es-le: e ≤loc e' ,
rev_implies: P ⇐ Q,
cand: A c∧ B,
less_than: a < b
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:A {}\mrightarrow{} EClass(B)]. \mforall{}[Y:A {}\mrightarrow{} EClass(A)].
rec-bind-class(X;Y) \mmember{} A {}\mrightarrow{} EClass(B) supposing not-self-starting\{i:l\}(Info;A;Y)
Date html generated:
2016_05_17-AM-00_28_37
Last ObjectModification:
2016_01_17-PM-07_04_53
Theory : event-ordering
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