Nuprl Lemma : local-pred-class_wf
∀[Info:Type]. ∀[P:es:EO+(Info) ⟶ E ⟶ 𝔹].
(local-pred-class(P) ∈ EClass({e':E|
(e' <loc e)
∧ (↑(P es e'))
∧ (∀e'':E. ((e' <loc e'') ⇒ (e'' <loc e) ⇒ (¬↑(P es e''))))} ))
Proof
Definitions occuring in Statement :
local-pred-class: local-pred-class(P),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
local-pred-class: local-pred-class(P),
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x],
or: P ∨ Q,
sq_exists: ∃x:{A| B[x]}
Latex:
\mforall{}[Info:Type]. \mforall{}[P:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} \mBbbB{}].
(local-pred-class(P) \mmember{} EClass(\{e':E|
(e' <loc e)
\mwedge{} (\muparrow{}(P es e'))
\mwedge{} (\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} (e'' <loc e) {}\mRightarrow{} (\mneg{}\muparrow{}(P es e''))))\} ))
Date html generated:
2016_05_16-PM-11_27_04
Last ObjectModification:
2015_12_29-AM-10_23_49
Theory : event-ordering
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