Nuprl Lemma : es-init-identity
∀[es:EO]. ∀[e:E]. uiff(es-init(es;e) = e ∈ E;↑first(e))
Proof
Definitions occuring in Statement :
es-init: es-init(es;e),
es-first: first(e),
es-E: E,
event_ordering: EO,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
es-init: es-init(es;e),
final-iterate: final-iterate(f;x),
do-apply: do-apply(f;x),
can-apply: can-apply(f;x),
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
bfalse: ff,
isl: isl(x),
outl: outl(x),
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False
Latex:
\mforall{}[es:EO]. \mforall{}[e:E]. uiff(es-init(es;e) = e;\muparrow{}first(e))
Date html generated:
2016_05_16-AM-09_39_37
Last ObjectModification:
2015_12_28-PM-09_42_39
Theory : new!event-ordering
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