Nuprl Lemma : cs-inning-committed-single-stable

∀[V:Type]. ∀[A:Id List]. ∀[W:{a:Id| (a ∈ A)}  List List]. ∀[s,s2:ConsensusState].
  ∀[i:ℤ]. ∀[v,v2:V].
    (v = v2 ∈ V) supposing
       (in state s, inning i has committed v2 and
       in state s2, inning i could commit v  and
       two-intersection(A;W))
  supposing s ts-rel(consensus-ts4(V;A;W)) s2

Proof

Definitions occuring in Statement : two-intersection: two-intersection(A;W), cs-inning-committable: in state s, inning i could commit v , cs-inning-committed: in state s, inning i has committed v, consensus-ts4: consensus-ts4(V;A;W), consensus-state4: ConsensusState, Id: Id, l_member: (x ∈ l), list: T List, uimplies: b supposing a, uall: ∀[x:A]. B[x], infix_ap: x f y, set: {x:A| B[x]} , int: ℤ, universe: Type, equal: s = t ∈ T, ts-rel: ts-rel(ts)
Definitions unfolded in proof : uall: ∀[x:A]. B[x], member: t ∈ T, uimplies: b supposing a, prop: ℙ, infix_ap: x f y, subtype_rel: A ⊆r B, consensus-state4: ConsensusState, ts-type: ts-type(ts), pi1: fst(t), consensus-ts4: consensus-ts4(V;A;W), so_lambda: λ₂x.t[x], so_apply: x[s], all: ∀x:A. B[x], ts-stable: ts-stable(ts;x.P[x]), implies: P ⇒ Q

Latex:
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[W:\{a:Id| (a \mmember{} A)\} List List]. \mforall{}[s,s2:ConsensusState]. \mforall{}[i:\mBbbZ{}]. \mforall{}[v,v2:V]. (v = v2) supposing (in state s, inning i has committed v2 and in state s2, inning i could commit v and two-intersection(A;W)) supposing s ts-rel(consensus-ts4(V;A;W)) s2 Date html generated: 2016_05_16-PM-00_04_25 Last ObjectModification: 2015_12_29-PM-01_22_49 Theory : event-ordering Home Index