Nuprl Lemma : int-decr-map-remove-prop
∀[Value:Type]. ∀[m:int-decr-map-type(Value)]. ∀[k1,k2:ℤ].
(int-decr-map-find(k1;int-decr-map-remove(k2;m))
= if (k1 =z k2) then inr ⋅ else int-decr-map-find(k1;m) fi
∈ (Value?))
Proof
Definitions occuring in Statement :
int-decr-map-remove: int-decr-map-remove(k;m),
int-decr-map-find: int-decr-map-find(k;m),
int-decr-map-type: int-decr-map-type(Value),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
it: ⋅,
uall: ∀[x:A]. B[x],
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,
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,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
int-decr-map-find: int-decr-map-find(k;m),
find-combine: find-combine(cmp;l),
list_ind: list_ind,
int-decr-map-remove: int-decr-map-remove(k;m),
remove-combine: remove-combine(cmp;l),
nil: [],
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
cons: [a / b],
colength: colength(L),
decidable: Dec(P),
so_lambda: λ2x.t[x],
so_apply: x[s],
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nequal: a ≠ b ∈ T ,
has-value: (a)↓
Latex:
\mforall{}[Value:Type]. \mforall{}[m:int-decr-map-type(Value)]. \mforall{}[k1,k2:\mBbbZ{}].
(int-decr-map-find(k1;int-decr-map-remove(k2;m))
= if (k1 =\msubz{} k2) then inr \mcdot{} else int-decr-map-find(k1;m) fi )
Date html generated:
2016_05_17-PM-01_50_25
Last ObjectModification:
2016_01_17-AM-11_38_15
Theory : datatype-signatures
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