Nuprl Lemma : conditional_wf2
∀[T,V:Type]. ∀[A,B:T ⟶ ℙ]. ∀[dcd_A:t:T ⟶ Dec(A[t])]. ∀[f:{t:T| A[t]} ⟶ V]. ∀[g:{t:T| B[t]} ⟶ V].
([λt.A[t]? f : g] ∈ {t:T| A[t] ∨ B[t]} ⟶ V)
Proof
Definitions occuring in Statement :
conditional: [P? f : g],
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
or: P ∨ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s],
or: P ∨ Q,
prop: ℙ,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False
Latex:
\mforall{}[T,V:Type]. \mforall{}[A,B:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[dcd$_{A}$:t:T {}\mrightarrow{} Dec(A[t])]. \mforall{}[f:\{t:T| A[t]\} {}\mrightarrow{} V\000C]. \mforall{}[g:\{t:T| B[t]\} {}\mrightarrow{} V].
([\mlambda{}t.A[t]? f : g] \mmember{} \{t:T| A[t] \mvee{} B[t]\} {}\mrightarrow{} V)
Date html generated:
2016_05_16-AM-10_15_13
Last ObjectModification:
2015_12_28-PM-09_26_01
Theory : new!event-ordering
Home
Index