Nuprl Lemma : es-interval-induction2
∀es:EO. ∀i:Id.
∀[P:e1:{e:E| loc(e) = i ∈ Id} ⟶ {e2:E| loc(e2) = i ∈ Id} ⟶ ℙ]
(∀e1@i.∀e2≥e1.(∀e:E. ((e1 <loc e) ⇒ e ≤loc e2 ⇒ P[e;e2])) ⇒ P[e1;e2]
⇒ ∀e1@i.∀e2<e1.P[e1;e2]
⇒ (∀e,e':E. (P[e;e']) supposing ((loc(e') = i ∈ Id) and (loc(e) = i ∈ Id))))
Proof
Definitions occuring in Statement :
alle-lt: ∀e<e'.P[e],
alle-ge: ∀e'≥e.P[e'],
alle-at: ∀e@i.P[e],
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
alle-lt: ∀e<e'.P[e],
alle-at: ∀e@i.P[e],
alle-ge: ∀e'≥e.P[e'],
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
member: t ∈ T,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
es-locl: (e <loc e'),
subtype_rel: A ⊆r B,
so_apply: x[s],
guard: {T}
Latex:
\mforall{}es:EO. \mforall{}i:Id.
\mforall{}[P:e1:\{e:E| loc(e) = i\} {}\mrightarrow{} \{e2:E| loc(e2) = i\} {}\mrightarrow{} \mBbbP{}]
(\mforall{}e1@i.\mforall{}e2\mgeq{}e1.(\mforall{}e:E. ((e1 <loc e) {}\mRightarrow{} e \mleq{}loc e2 {}\mRightarrow{} P[e;e2])) {}\mRightarrow{} P[e1;e2]
{}\mRightarrow{} \mforall{}e1@i.\mforall{}e2<e1.P[e1;e2]
{}\mRightarrow{} (\mforall{}e,e':E. (P[e;e']) supposing ((loc(e') = i) and (loc(e) = i))))
Date html generated:
2016_05_16-AM-09_51_28
Last ObjectModification:
2015_12_28-PM-09_36_10
Theory : new!event-ordering
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