Nuprl Lemma : loc-on-path-cons
∀es:EO. ∀L:E List. ∀e:E. ∀i:Id. (loc-on-path(es;i;[e / L]) ⇐⇒ (loc(e) = i ∈ Id) ∨ loc-on-path(es;i;L))
Proof
Definitions occuring in Statement :
loc-on-path: loc-on-path(es;i;L),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
cons: [a / b],
list: T List,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
member: t ∈ T,
top: Top,
so_apply: x[s1;s2;s3],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
guard: {T},
rev_implies: P ⇐ Q,
loc-on-path: loc-on-path(es;i;L)
Latex:
\mforall{}es:EO. \mforall{}L:E List. \mforall{}e:E. \mforall{}i:Id. (loc-on-path(es;i;[e / L]) \mLeftarrow{}{}\mRightarrow{} (loc(e) = i) \mvee{} loc-on-path(es;i;L))
Date html generated:
2016_05_16-AM-09_53_52
Last ObjectModification:
2015_12_28-PM-09_33_15
Theory : new!event-ordering
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