Nuprl Lemma : compose-lattice-hom
∀[l1,l2,l3:Lattice]. ∀[f:Hom(l1;l2)]. ∀[g:Hom(l2;l3)]. (g o f ∈ Hom(l1;l3))
Proof
Definitions occuring in Statement :
lattice-hom: Hom(l1;l2),
lattice: Lattice,
compose: f o g,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lattice-hom: Hom(l1;l2),
lattice: Lattice,
and: P ∧ Q,
cand: A c∧ B,
compose: f o g,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
compose_wf,
lattice-point_wf,
uall_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
lattice-hom_wf,
lattice_wf,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
extract_by_obid,
isectElimination,
because_Cache,
hypothesis,
hypothesisEquality,
functionExtensionality,
applyEquality,
sqequalRule,
independent_pairFormation,
productElimination,
independent_pairEquality,
axiomEquality,
isect_memberEquality,
lambdaEquality,
productEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[l1,l2,l3:Lattice]. \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_23_51
Last ObjectModification:
2017_07_28-AM-09_12_33
Theory : lattices
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