Nuprl Lemma : es-prior-interface-cases
∀[Info:Type]
∀X:EClass(Top). ∀es:EO+(Info). ∀e:E.
(¬↑first(e))
∧ (((↑pred(e) ∈b X) ∧ (prior(X)(e) = pred(e) ∈ E))
∨ ((¬↑pred(e) ∈b X) ∧ (↑pred(e) ∈b prior(X)) ∧ (prior(X)(e) = prior(X)(pred(e)) ∈ E)))
supposing ↑e ∈b prior(X)
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e ∈b X,
do-apply: do-apply(f;x),
can-apply: can-apply(f;x),
local-pred-class: local-pred-class(P),
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
eclass: EClass(A[eo; e]),
nat: ℕ,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s],
or: P ∨ Q,
isl: isl(x),
outl: outl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
top: Top,
eq_int: (i =z j),
bfalse: ff,
sq_exists: ∃x:{A| B[x]},
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
uimplies: b supposing a,
true: True,
cand: A c∧ B,
not: ¬A,
false: False,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Info:Type]
\mforall{}X:EClass(Top). \mforall{}es:EO+(Info). \mforall{}e:E.
(\mneg{}\muparrow{}first(e))
\mwedge{} (((\muparrow{}pred(e) \mmember{}\msubb{} X) \mwedge{} (prior(X)(e) = pred(e)))
\mvee{} ((\mneg{}\muparrow{}pred(e) \mmember{}\msubb{} X) \mwedge{} (\muparrow{}pred(e) \mmember{}\msubb{} prior(X)) \mwedge{} (prior(X)(e) = prior(X)(pred(e)))))
supposing \muparrow{}e \mmember{}\msubb{} prior(X)
Date html generated:
2016_05_16-PM-11_51_06
Last ObjectModification:
2015_12_29-AM-10_15_43
Theory : event-ordering
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