Nuprl Lemma : int_loset_wf
int_loset() ∈ LOSet
Proof
Definitions occuring in Statement :
int_loset: int_loset()
,
loset: LOSet
,
member: t ∈ T
Definitions unfolded in proof :
int_loset: int_loset()
,
member: t ∈ T
,
uall: ∀[x:A]. B[x]
,
uimplies: b supposing a
,
eqfun_p: IsEqFun(T;eq)
,
infix_ap: x f y
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
prop: ℙ
,
subtype_rel: A ⊆r B
,
implies: P
⇒ Q
,
iff: P
⇐⇒ Q
,
rev_implies: P
⇐ Q
,
so_lambda: λ2x.t[x]
,
so_apply: x[s]
,
so_lambda: λ2x y.t[x; y]
,
so_apply: x[s1;s2]
,
le: A ≤ B
,
not: ¬A
,
false: False
,
ulinorder: UniformLinorder(T;x,y.R[x; y])
,
uorder: UniformOrder(T;x,y.R[x; y])
,
urefl: UniformlyRefl(T;x,y.E[x; y])
,
all: ∀x:A. B[x]
,
decidable: Dec(P)
,
or: P ∨ Q
,
satisfiable_int_formula: satisfiable_int_formula(fmla)
,
exists: ∃x:A. B[x]
,
top: Top
,
utrans: UniformlyTrans(T;x,y.E[x; y])
,
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y])
,
connex: Connex(T;x,y.R[x; y])
Lemmas referenced :
mk_oset_wf,
eq_int_wf,
le_int_wf,
equal-wf-base,
int_subtype_base,
iff_weakening_uiff,
assert_wf,
assert_of_eq_int,
assert_witness,
uall_wf,
uiff_wf,
ulinorder_functionality_wrt_iff,
le_wf,
assert_of_le_int,
less_than'_wf,
decidable__le,
satisfiable-full-omega-tt,
intformnot_wf,
intformle_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
intformand_wf,
int_formula_prop_and_lemma,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
decidable__or,
intformor_wf,
int_formula_prop_or_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
lambdaEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
isect_memberFormation,
independent_pairFormation,
applyEquality,
because_Cache,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
addLevel,
uallFunctionality,
independent_functionElimination,
cumulativity,
instantiate,
dependent_functionElimination,
voidElimination,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
voidEquality,
computeAll,
lambdaFormation
Latex:
int\_loset() \mmember{} LOSet
Date html generated:
2017_10_01-AM-08_13_23
Last ObjectModification:
2017_02_28-PM-01_57_59
Theory : sets_1
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