Nuprl Lemma : es-p-locl_transitivity
∀es:EO. ∀p:E ⟶ (E + Top). ∀a,b,c:E. (a p< b ⇒ b p< c ⇒ a p< c)
Proof
Definitions occuring in Statement :
es-p-locl: e p< e',
es-E: E,
event_ordering: EO,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
union: left + right
Definitions unfolded in proof :
es-p-locl: e p< e',
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
and: P ∧ Q,
p-graph: p-graph(A;f),
cand: A c∧ B,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
do-apply: do-apply(f;x),
nat: ℕ,
squash: ↓T
Latex:
\mforall{}es:EO. \mforall{}p:E {}\mrightarrow{} (E + Top). \mforall{}a,b,c:E. (a p< b {}\mRightarrow{} b p< c {}\mRightarrow{} a p< c)
Date html generated:
2016_05_16-AM-10_30_21
Last ObjectModification:
2016_01_17-PM-01_22_43
Theory : new!event-ordering
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