Nuprl Lemma : member-parallel-class
∀[Info,A:Type]. ∀[X,Y:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. uiff(↑e ∈b X || Y;↑(e ∈b X ∨be ∈b Y))
Proof
Definitions occuring in Statement :
parallel-class: X || Y,
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
bor: p ∨bq,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
parallel-class: X || Y,
member-eclass: e ∈b X,
eclass-compose2: eclass-compose2(f;X;Y),
eclass: EClass(A[eo; e]),
nat: ℕ,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
all: ∀x:A. B[x],
top: Top,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
guard: {T},
ge: i ≥ j
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X,Y:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. uiff(\muparrow{}e \mmember{}\msubb{} X || Y;\muparrow{}(e \mmember{}\msubb{} X \mvee{}\msubb{}e \mmember{}\msubb{} Y))
Date html generated:
2016_05_17-AM-11_12_30
Last ObjectModification:
2016_01_18-AM-00_10_28
Theory : process-model
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