Nuprl Lemma : simple-comb-2-es-sv
∀[Info,A,B,C:Type]. ∀[es:EO+(Info)]. ∀[F:A ⟶ B ⟶ C]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
(es-sv-class(es;lifting-2(F)|X, Y|)) supposing (es-sv-class(es;Y) and es-sv-class(es;X))
Proof
Definitions occuring in Statement :
simple-comb-2: F|X, Y|,
es-sv-class: es-sv-class(es;X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
lifting-2: lifting-2(f)
Definitions unfolded in proof :
simple-comb-2: F|X, Y|,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
int_seg: {i..j-},
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
select: L[n],
cons: [a / b],
subtract: n - m,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
less_than: a < b,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
eclass: EClass(A[eo; e]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-sv-class: es-sv-class(es;X),
lifting-2: lifting-2(f),
lifting2: lifting2(f;abag;bbag),
lifting-gen-rev: lifting-gen-rev(n;f;bags),
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
ge: i ≥ j ,
cand: A c∧ B,
iff: P ⇐⇒ Q
Latex:
\mforall{}[Info,A,B,C:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[F:A {}\mrightarrow{} B {}\mrightarrow{} C]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)].
(es-sv-class(es;lifting-2(F)|X, Y|)) supposing (es-sv-class(es;Y) and es-sv-class(es;X))
Date html generated:
2016_05_17-AM-09_29_55
Last ObjectModification:
2016_01_17-PM-11_14_47
Theory : classrel!lemmas
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