Nuprl Lemma : es-interface-match_wf
∀[Info,Ta,Tb:Type]. ∀[A:EClass(Ta)]. ∀[B:EClass(Tb)]. ∀[R:Ta ⟶ Tb ⟶ 𝔹]. (es-interface-match(A;B;R) ∈ EClass(Ta × Tb))
Proof
Definitions occuring in Statement :
es-interface-match: es-interface-match(A;B;R),
eclass: EClass(A[eo; e]),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
es-interface-match: es-interface-match(A;B;R),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
nat: ℕ,
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
sq_exists: ∃x:{A| B[x]},
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,Ta,Tb:Type]. \mforall{}[A:EClass(Ta)]. \mforall{}[B:EClass(Tb)]. \mforall{}[R:Ta {}\mrightarrow{} Tb {}\mrightarrow{} \mBbbB{}].
(es-interface-match(A;B;R) \mmember{} EClass(Ta \mtimes{} Tb))
Date html generated:
2016_05_17-AM-06_43_47
Last ObjectModification:
2016_01_17-PM-06_32_25
Theory : event-ordering
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