Nuprl Lemma : flattice-equiv_wf
∀[X:Type]. ∀[x,y:Point(free-dl(X + X))]. (flattice-equiv(X;x;y) ∈ ℙ)
Proof
Definitions occuring in Statement :
flattice-equiv: flattice-equiv(X;x;y),
free-dl: free-dl(X),
lattice-point: Point(l),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
flattice-equiv: flattice-equiv(X;x;y),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
lattice-point: Point(l),
record-select: r.x,
free-dl: free-dl(X),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
free-dl-type: free-dl-type(X),
quotient: x,y:A//B[x; y],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
so_apply: x[s],
bdd-distributive-lattice: BoundedDistributiveLattice
Lemmas referenced :
squash_wf,
exists_wf,
list_wf,
equal_wf,
subtype_quotient,
dlattice-eq_wf,
dlattice-eq-equiv,
flattice-order_wf,
lattice-point_wf,
free-dl_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
uall_wf,
lattice-meet_wf,
lattice-join_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesis,
lambdaEquality,
productEquality,
hypothesisEquality,
applyEquality,
unionEquality,
cumulativity,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[X:Type]. \mforall{}[x,y:Point(free-dl(X + X))]. (flattice-equiv(X;x;y) \mmember{} \mBbbP{})
Date html generated:
2017_10_05-AM-00_44_00
Last ObjectModification:
2017_07_28-AM-09_18_22
Theory : lattices
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