Nuprl Lemma : int-decr-map-add_wf
∀[Value:Type]. ∀[k:ℤ]. ∀[v:Value]. ∀[m:int-decr-map-type(Value)]. (int-decr-map-add(k;v;m) ∈ int-decr-map-type(Value))
Proof
Definitions occuring in Statement :
int-decr-map-add: int-decr-map-add(k;v;m),
int-decr-map-type: int-decr-map-type(Value),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int-decr-map-type: int-decr-map-type(Value),
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
pi1: fst(t),
so_apply: x[s1;s2],
gt: i > j,
subtype_rel: A ⊆r B,
or: P ∨ Q,
iff: P ⇐⇒ Q,
true: True,
cons: [a / b],
colength: colength(L),
guard: {T},
decidable: Dec(P),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
int-decr-map-add: int-decr-map-add(k;v;m),
insert-combine: insert-combine(cmp;f;x;l),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
int-minus-comparison: int-minus-comparison(f),
has-value: (a)↓,
ifthenelse: if b then t else f fi ,
btrue: tt,
uiff: uiff(P;Q),
bfalse: ff,
rev_implies: P ⇐ Q,
cand: A c∧ B,
nequal: a ≠ b ∈ T ,
pi2: snd(t)
Latex:
\mforall{}[Value:Type]. \mforall{}[k:\mBbbZ{}]. \mforall{}[v:Value]. \mforall{}[m:int-decr-map-type(Value)].
(int-decr-map-add(k;v;m) \mmember{} int-decr-map-type(Value))
Date html generated:
2016_05_17-PM-01_49_45
Last ObjectModification:
2016_01_17-AM-11_37_36
Theory : datatype-signatures
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