Nuprl Lemma : compose-bounded-lattice-hom
∀[l1,l2,l3:BoundedLattice]. ∀[f:Hom(l1;l2)]. ∀[g:Hom(l2;l3)]. (g o f ∈ Hom(l1;l3))
Proof
Definitions occuring in Statement :
bounded-lattice-hom: Hom(l1;l2),
bdd-lattice: BoundedLattice,
compose: f o g,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bounded-lattice-hom: Hom(l1;l2),
and: P ∧ Q,
subtype_rel: A ⊆r B,
cand: A c∧ B,
lattice-hom: Hom(l1;l2),
bdd-lattice: BoundedLattice,
prop: ℙ,
compose: f o g,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
compose-lattice-hom,
bdd-lattice-subtype-lattice,
equal_wf,
lattice-0_wf,
lattice-1_wf,
bounded-lattice-hom_wf,
bdd-lattice_wf,
and_wf,
lattice-point_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-axioms_wf,
bounded-lattice-structure-subtype
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
productElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
independent_pairFormation,
productEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isect_memberEquality,
hyp_replacement,
instantiate,
lambdaEquality,
cumulativity,
independent_isectElimination,
applyLambdaEquality
Latex:
\mforall{}[l1,l2,l3:BoundedLattice]. \mforall{}[f:Hom(l1;l2)]. \mforall{}[g:Hom(l2;l3)]. (g o f \mmember{} Hom(l1;l3))
Date html generated:
2020_05_20-AM-08_24_54
Last ObjectModification:
2017_07_28-AM-09_12_41
Theory : lattices
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