Nuprl Lemma : mk-DeMorgan-algebra-equal-bounded-lattice
∀[L:BoundedLatticeStructure]. ∀[n:Top]. (mk-DeMorgan-algebra(L;n) = L ∈ BoundedLatticeStructure)
Proof
Definitions occuring in Statement :
mk-DeMorgan-algebra: mk-DeMorgan-algebra(L;n),
bounded-lattice-structure: BoundedLatticeStructure,
uall: ∀[x:A]. B[x],
top: Top,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mk-DeMorgan-algebra: mk-DeMorgan-algebra(L;n),
bounded-lattice-structure: BoundedLatticeStructure,
record+: record+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
sq_type: SQType(T),
guard: {T},
record-select: r.x,
top: Top,
eq_atom: x =a y,
bfalse: ff,
lattice-point: Point(l),
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
false: False,
lattice-meet: a ∧ b,
lattice-join: a ∨ b,
lattice-1: 1,
lattice-0: 0,
prop: ℙ,
record: record(x.T[x]),
record-update: r[x := v]
Lemmas referenced :
istype-top,
bounded-lattice-structure_wf,
eq_atom_wf,
uiff_transitivity,
equal-wf-base,
bool_wf,
atom_subtype_base,
assert_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
rec_select_update_lemma,
istype-void,
lattice-point_wf,
bounded-lattice-structure-subtype,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
istype-assert,
lattice-meet_wf,
lattice-join_wf,
lattice-1_wf,
lattice-0_wf,
equal_wf,
subtype_rel_self,
top-subtype-record
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality_alt,
isectElimination,
thin,
hypothesisEquality,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
universeIsType,
equalitySymmetry,
dependentIntersectionEqElimination,
dependentIntersection_memberEquality,
functionExtensionality,
tokenEquality,
lambdaFormation_alt,
unionElimination,
equalityElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
atomEquality,
because_Cache,
independent_functionElimination,
productElimination,
independent_isectElimination,
instantiate,
cumulativity,
dependent_functionElimination,
equalityTransitivity,
voidElimination,
independent_pairFormation,
equalityIsType4,
functionIsType,
equalityIsType1,
impliesFunctionality,
voidEquality,
isect_memberEquality,
lambdaFormation,
functionEquality,
universeEquality,
dependentIntersectionElimination
Latex:
\mforall{}[L:BoundedLatticeStructure]. \mforall{}[n:Top]. (mk-DeMorgan-algebra(L;n) = L)
Date html generated:
2019_10_31-AM-07_22_37
Last ObjectModification:
2018_11_12-AM-09_22_15
Theory : lattices
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