Nuprl Lemma : complete_wf
∀[S:System]. (complete{i:l}(S) ∈ ℙ')
Proof
Definitions occuring in Statement :
complete: complete{i:l}(S),
System: System,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
complete: complete{i:l}(S),
member: t ∈ T,
prop: ℙ,
or: P ∨ Q,
l_exists: (∃x∈L. P[x]),
l_all: (∀x∈L.P[x]),
System: System,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
node: node,
pi2: snd(t),
pi1: fst(t),
int_seg: {i..j-},
uimplies: b supposing a,
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
so_apply: x[s]
Lemmas referenced :
System_wf,
all_wf,
int_seg_wf,
length_wf,
node_wf,
subtype_rel_universe1,
exists_wf,
dl-prop_wf,
dl-valid_wf,
dl-implies_wf,
dl-conj_wf,
select_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
dl_KS_wf,
worlds_wf,
dl_KS_subtype,
l_all_wf2,
l_member_wf,
pi1_wf_top,
list_wf,
dl_forces_wf,
btrue_wf,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalRule,
unionEquality,
universeIsType,
cut,
introduction,
extract_by_obid,
hypothesis,
thin,
instantiate,
sqequalHypSubstitution,
isectElimination,
closedConclusion,
natural_numberEquality,
because_Cache,
applyEquality,
lambdaEquality_alt,
inhabitedIsType,
lambdaFormation_alt,
productElimination,
equalityIstype,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
setElimination,
rename,
independent_isectElimination,
imageElimination,
unionElimination,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
functionEquality,
productEquality,
independent_pairEquality,
setIsType,
functionIsType,
cumulativity
Latex:
\mforall{}[S:System]. (complete\{i:l\}(S) \mmember{} \mBbbP{}')
Date html generated:
2019_10_16-AM-11_25_04
Last ObjectModification:
2019_05_09-PM-01_09_20
Theory : dynamic!logic
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