Nuprl Lemma : conditional-idempotent
∀[T,V:Type]. ∀[A:T ─→ ℙ]. ∀[dcd_A:t:T ─→ Dec(A t)]. ∀[g:T ─→ V]. ([A? g : g] = g ∈ (T ─→ V))
Proof
Definitions occuring in Statement :
conditional: [P? f : g],
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
decidable_wf,
equal_wf
\mforall{}[T,V:Type]. \mforall{}[A:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[dcd$_{A}$:t:T {}\mrightarrow{} Dec(A t)]. \mforall{}[g:T {}\mrightarrow{} V]. ([A? g : g\000C] = g)
Date html generated:
2015_07_17-AM-09_01_32
Last ObjectModification:
2015_01_27-PM-00_54_37
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