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
Lemmas :
lg-label_wf,
int_seg_wf,
lg-size_wf,
nat_wf,
lg-all_wf,
all_wf,
ldag_wf
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:
2015_07_23-AM-11_04_36
Last ObjectModification:
2015_01_28-PM-11_34_04
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