Nuprl Lemma : simple-comb-4_wf
∀[Info,A,B,C,D,E:Type].
∀F:bag(A) ⟶ bag(B) ⟶ bag(C) ⟶ bag(D) ⟶ bag(E)
∀[W:EClass(A)]. ∀[X:EClass(B)]. ∀[Y:EClass(C)]. ∀[Z:EClass(D)]. (simple-comb-4(F;W;X;Y;Z) ∈ EClass(E))
Proof
Definitions occuring in Statement :
simple-comb-4: simple-comb-4(F;W;X;Y;Z),
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
simple-comb-4: simple-comb-4(F;W;X;Y;Z),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
sq_type: SQType(T),
select: L[n],
cons: [a / b],
subtract: n - m,
less_than: a < b,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,B,C,D,E:Type].
\mforall{}F:bag(A) {}\mrightarrow{} bag(B) {}\mrightarrow{} bag(C) {}\mrightarrow{} bag(D) {}\mrightarrow{} bag(E)
\mforall{}[W:EClass(A)]. \mforall{}[X:EClass(B)]. \mforall{}[Y:EClass(C)]. \mforall{}[Z:EClass(D)].
(simple-comb-4(F;W;X;Y;Z) \mmember{} EClass(E))
Date html generated:
2016_05_17-AM-00_20_41
Last ObjectModification:
2016_01_17-PM-06_49_39
Theory : event-ordering
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