Nuprl Lemma : global-eo-eq-E
∀[L:(Id × Top) List]. ∀[a,b:E]. (a = b ~ (a =z b))
Proof
Definitions occuring in Statement :
global-eo: global-eo(L),
es-eq-E: e = e',
es-E: E,
Id: Id,
list: T List,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
top: Top,
product: x:A × B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
int_seg: {i..j-},
all: ∀x:A. B[x],
es-eq-E: e = e',
es-eq: es-eq(es),
global-eo: global-eo(L),
es-locless: es-locless(es;e1;e2),
mk-extended-eo: mk-extended-eo,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
mk-eo: mk-eo(E;dom;l;R;locless;pred;rank),
mk-eo-record: mk-eo-record(E;dom;l;R;locless;pred;rank),
btrue: tt,
infix_ap: x f y,
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ,
less_than: a < b,
squash: ↓T,
bool: 𝔹,
unit: Unit,
it: ⋅,
band: p ∧b q,
uiff: uiff(P;Q),
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B
Latex:
\mforall{}[L:(Id \mtimes{} Top) List]. \mforall{}[a,b:E]. (a = b \msim{} (a =\msubz{} b))
Date html generated:
2016_05_17-AM-08_28_54
Last ObjectModification:
2016_01_17-PM-02_33_12
Theory : event-ordering
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