Nuprl Lemma : cs-ref-map-equal
∀[V:Type]. ∀[A:Id List]. ∀[W:{a:Id| (a ∈ A)} List List]. ∀[f:ConsensusState ─→ (consensus-state3(V) List)].
∀[x,y:ConsensusState]. ∀[i:ℕ||f x||].
(f x[i] = f y[i] ∈ consensus-state3(V)) supposing
((∀v:V
((in state x, inning i could commit v ⇐⇒ in state y, inning i could commit v )
∧ (in state x, inning i has committed v ⇐⇒ in state y, inning i has committed v))) and
i < ||f y||)
supposing cs-ref-map-constraints(V;A;W;f)
Proof
Definitions occuring in Statement :
cs-ref-map-constraints: cs-ref-map-constraints(V;A;W;f),
cs-inning-committable: in state s, inning i could commit v ,
cs-inning-committed: in state s, inning i has committed v,
consensus-state4: ConsensusState,
consensus-state3: consensus-state3(T),
Id: Id,
l_member: (x ∈ l),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Lemmas :
cs-inning-committable_wf,
cs-inning-committed_wf,
int_seg_subtype-nat,
length_wf,
consensus-state3_wf,
false_wf,
all_wf,
iff_wf,
less_than_wf,
int_seg_wf,
consensus-state4_wf,
cs-ref-map-constraints_wf,
list_wf,
Id_wf,
l_member_wf,
exists_wf,
not_wf,
equal_wf,
equal-wf-T-base,
select_wf,
sq_stable__le,
cs-commited_wf,
cs-considering_wf,
consensus-state3-cases,
iff_weakening_equal
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[W:\{a:Id| (a \mmember{} A)\} List List].
\mforall{}[f:ConsensusState {}\mrightarrow{} (consensus-state3(V) List)].
\mforall{}[x,y:ConsensusState]. \mforall{}[i:\mBbbN{}||f x||].
(f x[i] = f y[i]) supposing
((\mforall{}v:V
((in state x, inning i could commit v \mLeftarrow{}{}\mRightarrow{} in state y, inning i could commit v )
\mwedge{} (in state x, inning i has committed v \mLeftarrow{}{}\mRightarrow{} in state y, inning i has committed v))) and
i < ||f y||)
supposing cs-ref-map-constraints(V;A;W;f)
Date html generated:
2015_07_17-AM-11_32_18
Last ObjectModification:
2015_02_04-PM-04_59_53
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