Nuprl Lemma : simple-comb-1-classrel
∀[Info,B,C:Type]. ∀[f:B ⟶ C]. ∀[X:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
uiff(v ∈ lifting-1(f)|X|(e);↓∃b:B. ((v = (f b) ∈ C) ∧ b ∈ X(e)))
Proof
Definitions occuring in Statement :
simple-comb-1: F|X|,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
lifting-1: lifting-1(f)
Definitions unfolded in proof :
lifting-1: lifting-1(f),
simple-comb-1: F|X|,
uall: ∀[x:A]. B[x],
member: t ∈ T,
simple-comb1: λx.F[x]|X|,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
exists: ∃x:A. B[x],
cand: A c∧ B,
prop: ℙ,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
sq_type: SQType(T),
select: L[n],
cons: [a / b],
less_than: a < b,
true: True,
subtype_rel: A ⊆r B,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[f:B {}\mrightarrow{} C]. \mforall{}[X:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:C].
uiff(v \mmember{} lifting-1(f)|X|(e);\mdownarrow{}\mexists{}b:B. ((v = (f b)) \mwedge{} b \mmember{} X(e)))
Date html generated:
2016_05_17-AM-09_20_48
Last ObjectModification:
2016_01_17-PM-11_12_33
Theory : classrel!lemmas
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