Nuprl Lemma : int-decr-map-isEmpty-assert
∀[Value:Type]. ∀[m:int-decr-map-type(Value)].
uiff(↑int-decr-map-isEmpty(m);m = int-decr-map-empty() ∈ int-decr-map-type(Value))
Proof
Definitions occuring in Statement :
int-decr-map-isEmpty: int-decr-map-isEmpty(m),
int-decr-map-empty: int-decr-map-empty(),
int-decr-map-type: int-decr-map-type(Value),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
int-decr-map-isEmpty: int-decr-map-isEmpty(m),
int-decr-map-type: int-decr-map-type(Value),
int-decr-map-empty: int-decr-map-empty(),
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
top: Top,
so_apply: x[s1;s2],
gt: i > j,
prop: ℙ,
assert: ↑b,
ifthenelse: if b then t else f fi ,
null: null(as),
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
strict4: strict4(F),
implies: P ⇒ Q,
has-value: (a)↓,
guard: {T},
or: P ∨ Q,
squash: ↓T,
nil: [],
it: ⋅,
btrue: tt,
true: True,
pi1: fst(t),
sq_stable: SqStable(P)
Latex:
\mforall{}[Value:Type]. \mforall{}[m:int-decr-map-type(Value)].
uiff(\muparrow{}int-decr-map-isEmpty(m);m = int-decr-map-empty())
Date html generated:
2016_05_17-PM-01_48_41
Last ObjectModification:
2016_01_18-PM-06_42_25
Theory : datatype-signatures
Home
Index