Nuprl Lemma : divisibility-lattice_wf
divisibility-lattice() ∈ Lattice
Proof
Definitions occuring in Statement :
divisibility-lattice: divisibility-lattice(),
lattice: Lattice,
member: t ∈ T
Definitions unfolded in proof :
divisibility-lattice: divisibility-lattice(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
all: ∀x:A. B[x],
prop: ℙ,
uimplies: b supposing a,
so_apply: x[s1;s2],
and: P ∧ Q,
cand: A c∧ B,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
label: ...$L... t,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top
Lemmas referenced :
mk-lattice_wf,
nat_wf,
gcd_wf,
gcd-non-neg,
le_wf,
lcm_wf_nat,
gcd_sym_nat,
zero-le-nat,
equal_wf,
squash_wf,
true_wf,
lcm-com-nat,
lcm_wf,
iff_weakening_equal,
gcd_assoc_nat,
trivial-equal,
lcm-assoc-nat,
lcm-gcd-absorption,
nat_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__le,
intformle_wf,
itermConstant_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
gcd-lcm-absorption
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
dependent_set_memberEquality,
dependent_functionElimination,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
because_Cache,
independent_isectElimination,
sqequalRule,
isect_memberFormation,
isect_memberEquality,
axiomEquality,
independent_pairFormation,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
intEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
voidElimination,
voidEquality,
computeAll
Latex:
divisibility-lattice() \mmember{} Lattice
Date html generated:
2020_05_20-AM-08_24_00
Last ObjectModification:
2017_07_28-AM-09_12_36
Theory : lattices
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