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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