Nuprl Lemma : existse-le-iff
∀es:EO. ∀e':E. ∀[P:{e:E| loc(e) = loc(e') ∈ Id} ⟶ ℙ]. (∃e≤e'.P[e] ⇐⇒ P[e'] ∨ ∃e<e'.P[e])
Proof
Definitions occuring in Statement :
existse-before: ∃e<e'.P[e],
existse-le: ∃e≤e'.P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: 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],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
existse-le: ∃e≤e'.P[e],
exists: ∃x:A. B[x],
cand: A c∧ B,
es-le: e ≤loc e' ,
or: P ∨ Q,
guard: {T},
existse-before: ∃e<e'.P[e],
es-locl: (e <loc e'),
subtype_rel: A ⊆r B,
squash: ↓T,
uimplies: b supposing a
Latex:
\mforall{}es:EO. \mforall{}e':E. \mforall{}[P:\{e:E| loc(e) = loc(e')\} {}\mrightarrow{} \mBbbP{}]. (\mexists{}e\mleq{}e'.P[e] \mLeftarrow{}{}\mRightarrow{} P[e'] \mvee{} \mexists{}e<e'.P[e])
Date html generated:
2016_05_16-AM-09_41_38
Last ObjectModification:
2016_01_17-PM-01_26_05
Theory : new!event-ordering
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