Nuprl Lemma : assert-cs-is-considering
∀[V:Type]. ∀x:consensus-state3(V). (↑cs-is-considering(x) ⇐⇒ ∃v:V. (x = CONSIDERING[v] ∈ consensus-state3(V)))
Proof
Definitions occuring in Statement :
cs-is-considering: cs-is-considering(x),
cs-considering: CONSIDERING[v],
consensus-state3: consensus-state3(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
assert_wf,
bfalse_wf,
isl_wf,
bool_wf,
and_wf,
equal_wf,
btrue_wf,
btrue_neq_bfalse,
iff_imp_equal_bool,
subtype_base_sq,
bool_subtype_base,
true_wf,
assert_witness,
exists_wf
\mforall{}[V:Type]. \mforall{}x:consensus-state3(V). (\muparrow{}cs-is-considering(x) \mLeftarrow{}{}\mRightarrow{} \mexists{}v:V. (x = CONSIDERING[v]))
Date html generated:
2015_07_17-AM-11_23_34
Last ObjectModification:
2015_01_28-AM-07_30_41
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