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
Lemmas :
conditional_wf,
or_wf,
subtype_rel_dep_function,
decidable_wf,
subtype_rel_self,
set_wf,
subtype_rel_nested_set2,
subtype_rel_sets,
not_wf
\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:
2015_07_17-AM-09_01_26
Last ObjectModification:
2015_01_27-PM-00_56_19
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