Nuprl Lemma : es-loc-pred-plus
∀[es:EO]. ∀[x,y:E]. loc(x) = loc(y) ∈ Id supposing x λx,y. ((¬↑first(y)) c∧ (x = pred(y) ∈ E))+ y
Proof
Definitions occuring in Statement :
es-first: first(e),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
rel_plus: R+,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
infix_ap: x f y,
not: ¬A,
lambda: λx.A[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rel_plus: R+,
infix_ap: x f y,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
cand: A c∧ B,
es-E: E,
es-base-E: es-base-E(es),
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
less_than': less_than'(a;b),
rel_exp: R^n,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
int_upper: {i...},
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[es:EO]. \mforall{}[x,y:E]. loc(x) = loc(y) supposing x \mlambda{}x,y. ((\mneg{}\muparrow{}first(y)) c\mwedge{} (x = pred(y)))\msupplus{} y
Date html generated:
2016_05_16-AM-09_17_45
Last ObjectModification:
2016_01_17-PM-01_31_10
Theory : new!event-ordering
Home
Index