Nuprl Lemma : es-init-elim2
∀[es:EO]. ∀[e:E]. es-init(es;e) ~ es-init(es;pred(e)) supposing ¬↑first(e)
Proof
Definitions occuring in Statement :
es-init: es-init(es;e),
es-first: first(e),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
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],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
not: ¬A,
false: False,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
isl: isl(x),
outl: outl(x)
Latex:
\mforall{}[es:EO]. \mforall{}[e:E]. es-init(es;e) \msim{} es-init(es;pred(e)) supposing \mneg{}\muparrow{}first(e)
Date html generated:
2016_05_16-AM-09_39_50
Last ObjectModification:
2015_12_28-PM-09_43_18
Theory : new!event-ordering
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