Nuprl Lemma : member-eclass-eclass3
∀[Info,B,C:Type]. ∀[X:EClass(B ⟶ C)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(↑e ∈b eclass3(X;Y);(↑e ∈b X) ∧ (↑e ∈b Y))
Proof
Definitions occuring in Statement :
eclass3: eclass3(X;Y),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ,
rev_uimplies: rev_uimplies(P;Q),
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} C)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} eclass3(X;Y);(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\muparrow{}e \mmember{}\msubb{} Y))
Date html generated:
2016_05_17-AM-11_14_54
Last ObjectModification:
2016_01_18-AM-00_10_46
Theory : process-model
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