Nuprl Lemma : decidable__existse-between3
∀es:EO. ∀e1,e2:E.
∀[P:{e:E| (loc(e) = loc(e1) ∈ Id) ∧ (¬↑first(e))} ─→ ℙ]
∀e@loc(e1).Dec(P[e]) supposing ¬↑first(e) ⇒ Dec(∃e∈(e1,e2].P[e]) supposing loc(e2) = loc(e1) ∈ Id
Proof
Definitions occuring in Statement :
existse-between3: ∃e∈(e1,e2].P[e],
alle-at: ∀e@i.P[e],
es-first: first(e),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
assert: ↑b,
decidable: Dec(P),
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,
and: P ∧ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
alle-at_wf,
Id_wf,
es-loc_wf,
es-E_wf,
isect_wf,
not_wf,
assert_wf,
es-first_wf2,
decidable_wf,
equal_wf,
event_ordering_wf,
decidable__existse-le,
es-locl_wf,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
decidable__cand,
decidable__es-locl,
es-le_wf,
exists_wf,
es-le-loc,
subtype_base_sq,
bool_wf,
bool_subtype_base,
false_wf
\mforall{}es:EO. \mforall{}e1,e2:E.
\mforall{}[P:\{e:E| (loc(e) = loc(e1)) \mwedge{} (\mneg{}\muparrow{}first(e))\} {}\mrightarrow{} \mBbbP{}]
\mforall{}e@loc(e1).Dec(P[e]) supposing \mneg{}\muparrow{}first(e) {}\mRightarrow{} Dec(\mexists{}e\mmember{}(e1,e2].P[e]) supposing loc(e2) = loc(e1)
Date html generated:
2015_07_17-AM-08_48_27
Last ObjectModification:
2015_01_27-PM-02_26_57
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