Nuprl Lemma : es-local-pred-iff-es-p-local-pred
∀[Info,T:Type].
∀X:EClass(T). ∀es:EO+(Info). ∀e,e':E.
uiff((last(λe'.0 <z #(X es e')) e) = (inl e') ∈ (E + Top);es-p-local-pred(es;λe'.inhabited-classrel(es;T;X;e')) e
e')
Proof
Definitions occuring in Statement :
es-local-pred: last(P),
inhabited-classrel: inhabited-classrel(eo;T;X;e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-p-local-pred: es-p-local-pred(es;P),
es-E: E,
lt_int: i <z j,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
apply: f a,
lambda: λx.A[x],
inl: inl x,
union: left + right,
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
bag-size: #(bs)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
eclass: EClass(A[eo; e]),
or: P ∨ Q,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
sq_exists: ∃x:{A| B[x]},
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
decidable: Dec(P),
le: A ≤ B,
less_than': less_than'(a;b),
nat: ℕ,
ge: i ≥ j ,
less_than: a < b,
squash: ↓T,
es-local-pred: last(P),
sq_type: SQType(T),
ifthenelse: if b then t else f fi ,
btrue: tt,
isl: isl(x),
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
es-p-local-pred: es-p-local-pred(es;P),
cand: A c∧ B,
true: True,
inhabited-classrel: inhabited-classrel(eo;T;X;e),
classrel: v ∈ X(e),
es-locl: (e <loc e'),
sq_stable: SqStable(P),
bool: 𝔹,
unit: Unit,
it: ⋅,
bnot: ¬bb,
assert: ↑b
Latex:
\mforall{}[Info,T:Type].
\mforall{}X:EClass(T). \mforall{}es:EO+(Info). \mforall{}e,e':E.
uiff((last(\mlambda{}e'.0 <z \#(X es e')) e)
= (inl e');es-p-local-pred(es;\mlambda{}e'.inhabited-classrel(es;T;X;e')) e e')
Date html generated:
2016_05_17-AM-09_27_18
Last ObjectModification:
2016_01_17-PM-11_12_57
Theory : classrel!lemmas
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