Nuprl Lemma : conditional_wf
∀[T,V:Type]. ∀[A:T ⟶ ℙ]. ∀[dcd_A:t:T ⟶ Dec(A t)]. ∀[f:{t:T| A t} ⟶ V]. ∀[g:{t:T| ¬(A t)} ⟶ V].
([A? f : g] ∈ T ⟶ V)
Proof
Definitions occuring in Statement :
conditional: [P? f : g],
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
not: ¬A,
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
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,
subtype_rel: A ⊆r B,
prop: ℙ
Latex:
\mforall{}[T,V:Type]. \mforall{}[A:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[dcd$_{A}$:t:T {}\mrightarrow{} Dec(A t)]. \mforall{}[f:\{t:T| A t\} {}\mrightarrow{} V]. \mforall{}\000C[g:\{t:T| \mneg{}(A t)\} {}\mrightarrow{} V].
([A? f : g] \mmember{} T {}\mrightarrow{} V)
Date html generated:
2016_05_16-AM-10_15_06
Last ObjectModification:
2015_12_28-PM-09_24_20
Theory : new!event-ordering
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