Nuprl Lemma : l_all-mapfilter-interface-predecessors
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A)]. ∀[Q:E(X) ⟶ 𝔹]. ∀[P:A ⟶ 𝔹]. ∀[e:E(X)].
uiff((∀v∈mapfilter(λe.X(e);λe'.Q[e'];≤(X)(e)).↑P[v]);∀e'≤e.(↑e' ∈b X) ⇒ (↑Q[e']) ⇒ (↑P[X(e')]))
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
alle-le: ∀e≤e'.P[e],
mapfilter: mapfilter(f;P;L),
l_all: (∀x∈L.P[x]),
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
uiff: uiff(P;Q),
and: P ∧ Q,
alle-le: ∀e≤e'.P[e],
implies: P ⇒ Q,
so_apply: x[s],
es-E-interface: E(X),
prop: ℙ,
so_lambda: λ2x.t[x],
sq_stable: SqStable(P),
squash: ↓T,
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
less_than: a < b,
iff: P ⇐⇒ Q,
cand: A c∧ B,
rev_implies: P ⇐ Q,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Q:E(X) {}\mrightarrow{} \mBbbB{}]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[e:E(X)].
uiff((\mforall{}v\mmember{}mapfilter(\mlambda{}e.X(e);\mlambda{}e'.Q[e'];\mleq{}(X)(e)).\muparrow{}P[v]);\mforall{}e'\mleq{}e.(\muparrow{}e' \mmember{}\msubb{} X) {}\mRightarrow{} (\muparrow{}Q[e']) {}\mRightarrow{} (\muparrow{}P[X(e')]))
Date html generated:
2016_05_17-AM-07_05_29
Last ObjectModification:
2016_01_17-PM-06_48_24
Theory : event-ordering
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