Nuprl Lemma : decidable-exists-finite
∀[T:Type]. ∀[P:T ⟶ ℙ]. ((∀x:T. Dec(P[x])) ⇒ finite-type(T) ⇒ Dec(∃x:T. P[x]))
Proof
Definitions occuring in Statement :
finite-type: finite-type(T),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
finite-type: finite-type(T),
exists: ∃x:A. B[x],
surject: Surj(A;B;f),
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
nat: ℕ,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T}
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x:T. Dec(P[x])) {}\mRightarrow{} finite-type(T) {}\mRightarrow{} Dec(\mexists{}x:T. P[x]))
Date html generated:
2016_05_16-AM-10_23_51
Last ObjectModification:
2015_12_28-PM-09_20_20
Theory : new!event-ordering
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