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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
conditional: [P? f : g],
branch: if p:P then A[p] else B fi ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q
Latex:
\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:
2016_05_16-AM-10_15_21
Last ObjectModification:
2015_12_28-PM-09_24_05
Theory : new!event-ordering
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