Nuprl Lemma : int-decr-map-find-not-in
∀[Value:Type]. ∀[k:ℤ]. ∀[m:int-decr-map-type(Value)].
int-decr-map-find(k;m) = (inr ⋅ ) ∈ (Value?) supposing (∀p∈m.¬(k = (fst(p)) ∈ ℤ))
Proof
Definitions occuring in Statement :
int-decr-map-find: int-decr-map-find(k;m),
int-decr-map-type: int-decr-map-type(Value),
l_all: (∀x∈L.P[x]),
it: ⋅,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
not: ¬A,
unit: Unit,
inr: inr x ,
union: left + right,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
int-decr-map-type: int-decr-map-type(Value),
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
pi1: fst(t),
so_apply: x[s1;s2],
gt: i > j,
or: P ∨ Q,
int-decr-map-find: int-decr-map-find(k;m),
find-combine: find-combine(cmp;l),
list_ind: list_ind,
nil: [],
it: ⋅,
cons: [a / b],
colength: colength(L),
guard: {T},
decidable: Dec(P),
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
iff: P ⇐⇒ Q,
has-value: (a)↓,
ifthenelse: if b then t else f fi ,
btrue: tt,
uiff: uiff(P;Q),
bfalse: ff
Latex:
\mforall{}[Value:Type]. \mforall{}[k:\mBbbZ{}]. \mforall{}[m:int-decr-map-type(Value)].
int-decr-map-find(k;m) = (inr \mcdot{} ) supposing (\mforall{}p\mmember{}m.\mneg{}(k = (fst(p))))
Date html generated:
2016_05_17-PM-01_48_13
Last ObjectModification:
2016_01_17-AM-11_37_38
Theory : datatype-signatures
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