Nuprl Lemma : opposite-lattice_wf
∀[L:BoundedDistributiveLattice]. (opposite-lattice(L) ∈ BoundedDistributiveLattice)
Proof
Definitions occuring in Statement :
opposite-lattice: opposite-lattice(L),
bdd-distributive-lattice: BoundedDistributiveLattice,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
opposite-lattice: opposite-lattice(L),
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
cand: A c∧ B,
guard: {T},
distributive-lattice: DistributiveLattice,
lattice: Lattice,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bdd-lattice: BoundedLattice,
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
bdd-distributive-lattice-subtype-distributive-lattice,
mk-bounded-distributive-lattice_wf,
lattice-point_wf,
bounded-lattice-structure-subtype,
lattice-join_wf,
lattice-meet_wf,
lattice-1_wf,
lattice-0_wf,
lattice_properties,
subtype_rel_sets,
lattice-structure_wf,
lattice-axioms_wf,
uall_wf,
equal_wf,
lattice-join-0,
bounded-lattice-axioms_wf,
squash_wf,
true_wf,
lattice-meet-1,
iff_weakening_equal,
distributive-lattice-dual-distrib,
bdd-distributive-lattice_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
applyEquality,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
sqequalRule,
setElimination,
thin,
rename,
productElimination,
isectElimination,
lambdaEquality,
because_Cache,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
instantiate,
productEquality,
cumulativity,
setEquality,
lambdaFormation,
isect_memberEquality,
axiomEquality,
independent_pairFormation,
dependent_set_memberEquality,
imageElimination,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[L:BoundedDistributiveLattice]. (opposite-lattice(L) \mmember{} BoundedDistributiveLattice)
Date html generated:
2017_10_05-AM-00_36_27
Last ObjectModification:
2017_07_28-AM-09_14_59
Theory : lattices
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