Nuprl Lemma : bm_T-key_wf
∀[T,Key:Type]. ∀[v:binary_map(T;Key)]. bm_T-key(v) ∈ Key supposing ↑bm_T?(v)
Proof
Definitions occuring in Statement :
bm_T-key: bm_T-key(v),
bm_T?: bm_T?(v),
binary_map: binary_map(T;Key),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bm_T?: bm_T?(v),
pi1: fst(t),
assert: ↑b,
bfalse: ff,
false: False,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
bm_T-key: bm_T-key(v),
pi2: snd(t)
Latex:
\mforall{}[T,Key:Type]. \mforall{}[v:binary\_map(T;Key)]. bm\_T-key(v) \mmember{} Key supposing \muparrow{}bm\_T?(v)
Date html generated:
2016_05_17-PM-01_37_24
Last ObjectModification:
2015_12_28-PM-08_11_01
Theory : binary-map
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