Nuprl Lemma : es-decl-set-join_wf
∀[dd1,dd2:DeclSet]. (es-decl-set-join(dd1;dd2) ∈ DeclSet)
Proof
Definitions occuring in Statement :
es-decl-set-join: es-decl-set-join(dd1;dd2),
es-decl-set: DeclSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
es-decl-set: DeclSet,
es-decl-set-join: es-decl-set-join(dd1;dd2),
spreadn: spread3,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
rev_implies: P ⇐ Q
Latex:
\mforall{}[dd1,dd2:DeclSet]. (es-decl-set-join(dd1;dd2) \mmember{} DeclSet)
Date html generated:
2016_05_16-PM-00_52_53
Last ObjectModification:
2016_01_17-PM-07_58_20
Theory : event-ordering
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