Nuprl Lemma : rec-bind-classrel2
∀[Info,A,B:Type]. ∀[X:A ⟶ EClass(B)]. ∀[Y:A ⟶ EClass(A)].
∀[es:EO+(Info)]. ∀[e:E]. ∀[a:A]. ∀[v:B].
uiff(v ∈ rec-bind-class(X;Y) a(e);↓v ∈ X a(e)
∨ (∃a':A. (a' ∈ Y a(e) ∧ v ∈ X a'(e)))
∨ (∃e':E. ∃a':A. ((e' <loc e) ∧ a' ∈ Y a(e') ∧ v ∈ rec-bind-class(X;Y) a'(e))))
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),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
and: P ∧ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
so_apply: x[s],
guard: {T},
sq_stable: SqStable(P),
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
uiff: uiff(P;Q),
squash: ↓T,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
le: A ≤ B,
less_than': less_than'(a;b),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
rec-bind-class: rec-bind-class(X;Y),
sq_or: a ↓∨ b,
mbind-class: X >>= Y,
es-le: e ≤loc e' ,
cand: A c∧ B,
true: True,
iff: P ⇐⇒ Q,
not-self-starting: not-self-starting{i:l}(Info;A;Y),
label: ...$L... t,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:A {}\mrightarrow{} EClass(B)]. \mforall{}[Y:A {}\mrightarrow{} EClass(A)].
\mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[a:A]. \mforall{}[v:B].
uiff(v \mmember{} rec-bind-class(X;Y) a(e);\mdownarrow{}v \mmember{} X a(e)
\mvee{} (\mexists{}a':A. (a' \mmember{} Y a(e) \mwedge{} v \mmember{} X a'(e)))
\mvee{} (\mexists{}e':E
\mexists{}a':A
((e' <loc e)
\mwedge{} a' \mmember{} Y a(e')
\mwedge{} v \mmember{} rec-bind-class(X;Y) a'(e))))
supposing not-self-starting\{i:l\}(Info;A;Y)
Date html generated:
2016_05_17-AM-10_07_11
Last ObjectModification:
2016_01_17-PM-11_11_42
Theory : classrel!lemmas
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