Nuprl Lemma : Set-isSet
∀[a:Set{i:l}]. isSet(a)
Proof
Definitions occuring in Statement :
isSet: isSet(w),
Set: Set{i:l},
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
and: P ∧ Q,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
nat: ℕ,
prop: ℙ,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
squash: ↓T,
all: ∀x:A. B[x],
coW-wfdd: coW-wfdd(a.B[a];w),
so_apply: x[s],
so_lambda: λ2x.t[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
Set: Set{i:l},
isSet: isSet(w)
Lemmas referenced :
W_wf,
copathAgree_wf,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
copath-length_wf,
equal_wf,
all_wf,
W-subtype-coW,
copath_wf,
nat_wf,
W-wfdd
Rules used in proof :
instantiate,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
int_eqEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
unionElimination,
natural_numberEquality,
addEquality,
dependent_set_memberEquality,
rename,
setElimination,
functionExtensionality,
intEquality,
applyEquality,
because_Cache,
cumulativity,
functionEquality,
setEquality,
baseClosed,
imageMemberEquality,
imageElimination,
dependent_functionElimination,
hypothesis,
hypothesisEquality,
lambdaEquality,
universeEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[a:Set\{i:l\}]. isSet(a)
Date html generated:
2018_07_29-AM-09_50_43
Last ObjectModification:
2018_07_24-PM-00_04_25
Theory : constructive!set!theory
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