Nuprl Lemma : disjoint-union-tr_wf
∀[A,B,S:Type]. ∀[tr1:Id ⟶ A ⟶ S ⟶ S]. ∀[tr2:Id ⟶ B ⟶ S ⟶ S]. (tr1 + tr2 ∈ Id ⟶ (A + B) ⟶ S ⟶ S)
Proof
Definitions occuring in Statement :
disjoint-union-tr: tr1 + tr2,
Id: Id,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
disjoint-union-tr: tr1 + tr2,
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,
outl: outl(x),
isl: isl(x),
assert: ↑b,
bfalse: ff,
false: False,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
outr: outr(x),
not: ¬A
Latex:
\mforall{}[A,B,S:Type]. \mforall{}[tr1:Id {}\mrightarrow{} A {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[tr2:Id {}\mrightarrow{} B {}\mrightarrow{} S {}\mrightarrow{} S].
(tr1 + tr2 \mmember{} Id {}\mrightarrow{} (A + B) {}\mrightarrow{} S {}\mrightarrow{} S)
Date html generated:
2016_05_17-AM-09_14_43
Last ObjectModification:
2015_12_29-PM-04_09_55
Theory : classrel!lemmas
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