Nuprl Lemma : lg-all_functionality
∀[T:Type]. ∀G:LabeledDAG(T). ∀[P1,P2:T ⟶ ℙ]. ((∀x:T. (P1[x] ⇒ P2[x])) ⇒ {∀x∈G.P1[x] ⇒ ∀x∈G.P2[x]})
Proof
Definitions occuring in Statement :
lg-all: ∀x∈G.P[x],
ldag: LabeledDAG(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
ldag: LabeledDAG(T),
implies: P ⇒ Q,
lg-all: ∀x∈G.P[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
nat: ℕ,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[T:Type]
\mforall{}G:LabeledDAG(T). \mforall{}[P1,P2:T {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x:T. (P1[x] {}\mRightarrow{} P2[x])) {}\mRightarrow{} \{\mforall{}x\mmember{}G.P1[x] {}\mRightarrow{} \mforall{}x\mmember{}G.P2[x]\})
Date html generated:
2016_05_17-AM-10_18_01
Last ObjectModification:
2015_12_29-PM-05_31_07
Theory : process-model
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