Nuprl Lemma : es-prior-interface-cases-sq
∀[Info:Type]
∀X:EClass(Top). ∀es:EO+(Info). ∀e:E.
(¬↑first(e))
∧ (((↑pred(e) ∈b X) ∧ (prior(X)(e) ~ pred(e)))
∨ ((¬↑pred(e) ∈b X) ∧ (↑pred(e) ∈b prior(X)) ∧ (prior(X)(e) ~ prior(X)(pred(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,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
exists: ∃x:A. B[x],
not: ¬A,
false: False,
prop: ℙ,
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
es-prior-interface: prior(X),
eclass-val: X(e),
local-pred-class: local-pred-class(P),
es-local-pred: last(P),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
in-eclass: e ∈b X,
eq_int: (i =z j),
eclass: EClass(A[eo; e]),
nat: ℕ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_exists: ∃x:{A| B[x]},
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) \msim{} pred(e)))
\mvee{} ((\mneg{}\muparrow{}pred(e) \mmember{}\msubb{} X) \mwedge{} (\muparrow{}pred(e) \mmember{}\msubb{} prior(X)) \mwedge{} (prior(X)(e) \msim{} prior(X)(pred(e)))))
supposing \muparrow{}e \mmember{}\msubb{} prior(X)
Date html generated:
2016_05_16-PM-11_51_29
Last ObjectModification:
2015_12_29-AM-10_12_46
Theory : event-ordering
Home
Index