Nuprl Lemma : id-is-bounded-lattice-hom
∀[l:BoundedLattice]. (λx.x ∈ Hom(l;l))
Proof
Definitions occuring in Statement :
bounded-lattice-hom: Hom(l1;l2),
bdd-lattice: BoundedLattice,
uall: ∀[x:A]. B[x],
member: t ∈ T,
lambda: λx.A[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bounded-lattice-hom: Hom(l1;l2),
and: P ∧ Q,
cand: A c∧ B,
bdd-lattice: BoundedLattice,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a,
lattice-hom: Hom(l1;l2)
Lemmas referenced :
lattice-0_wf,
lattice-1_wf,
equal_wf,
lattice-point_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
bdd-lattice_wf,
id-is-lattice-hom
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
independent_pairFormation,
because_Cache,
productEquality,
applyEquality,
instantiate,
lambdaEquality,
cumulativity,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[l:BoundedLattice]. (\mlambda{}x.x \mmember{} Hom(l;l))
Date html generated:
2017_10_05-AM-00_30_43
Last ObjectModification:
2017_07_28-AM-09_12_43
Theory : lattices
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