Nuprl Lemma : ranked-eo-eq-E
∀[L,rk:Top]. ∀[a,b:Top × ℤ]. (a = b ~ fst(a) = fst(b) ∧b (snd(a) =z snd(b)))
Proof
Definitions occuring in Statement :
ranked-eo: ranked-eo(L;rk),
es-eq-E: e = e',
eq_id: a = b,
band: p ∧b q,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
pi2: snd(t),
product: x:A × B[x],
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
es-eq-E: e = e',
es-eq: es-eq(es),
es-locless: es-locless(es;e1;e2),
top: Top,
ranked-eo: ranked-eo(L;rk),
mk-extended-eo: mk-extended-eo,
all: ∀x:A. B[x],
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,
pi1: fst(t),
pi2: snd(t),
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
prop: ℙ,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T}
Latex:
\mforall{}[L,rk:Top]. \mforall{}[a,b:Top \mtimes{} \mBbbZ{}]. (a = b \msim{} fst(a) = fst(b) \mwedge{}\msubb{} (snd(a) =\msubz{} snd(b)))
Date html generated:
2016_05_17-AM-08_43_37
Last ObjectModification:
2016_01_17-PM-02_28_53
Theory : event-ordering
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