Nuprl Lemma : alle-at-not-first
∀es:EO. ∀i:Id. ∀[P:{e:E| loc(e) = i ∈ Id} ⟶ ℙ]. (∀e@i.P[e] ⇒ ∀e@i.P[pred(e)] supposing ¬↑first(e))
Proof
Definitions occuring in Statement :
alle-at: ∀e@i.P[e],
es-first: first(e),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
alle-at: ∀e@i.P[e],
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
es-E: E,
es-base-E: es-base-E(es),
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}es:EO. \mforall{}i:Id. \mforall{}[P:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}]. (\mforall{}e@i.P[e] {}\mRightarrow{} \mforall{}e@i.P[pred(e)] supposing \mneg{}\muparrow{}first(e))
Date html generated:
2016_05_16-AM-09_40_29
Last ObjectModification:
2015_12_28-PM-09_42_29
Theory : new!event-ordering
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