Nuprl Lemma : map-sig-inDom-prop
∀[Key,Value:Type]. ∀[ms:map-sig{i:l}(Key;Value)]. ∀[k:Key]. ∀[m:map-sig-map(ms)].
(↑(map-sig-inDom(ms) k m) ⇐⇒ ↑isl(map-sig-find(ms) k m))
Proof
Definitions occuring in Statement :
map-sig-inDom: map-sig-inDom(m),
map-sig-find: map-sig-find(m),
map-sig-map: map-sig-map(m),
map-sig: map-sig{i:l}(Key;Value),
assert: ↑b,
isl: isl(x),
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
apply: f a,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
map-sig: map-sig{i:l}(Key;Value),
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
and: P ∧ Q,
prop: ℙ,
deq: EqDecider(T),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
band: p ∧b q,
not: ¬A,
cand: A c∧ B,
exposed-bfalse: exposed-bfalse,
squash: ↓T,
sq_stable: SqStable(P),
map-sig-find: map-sig-find(m),
map-sig-map: map-sig-map(m),
map-sig-inDom: map-sig-inDom(m)
Latex:
\mforall{}[Key,Value:Type]. \mforall{}[ms:map-sig\{i:l\}(Key;Value)]. \mforall{}[k:Key]. \mforall{}[m:map-sig-map(ms)].
(\muparrow{}(map-sig-inDom(ms) k m) \mLeftarrow{}{}\mRightarrow{} \muparrow{}isl(map-sig-find(ms) k m))
Date html generated:
2016_05_17-PM-01_47_20
Last ObjectModification:
2016_01_17-AM-11_37_39
Theory : datatype-signatures
Home
Index