Nuprl Lemma : compose-dma-hom
∀[dma1,dma2,dma3:DeMorganAlgebra]. ∀[f:dma-hom(dma1;dma2)]. ∀[g:dma-hom(dma2;dma3)]. (g o f ∈ dma-hom(dma1;dma3))
Proof
Definitions occuring in Statement :
dma-hom: dma-hom(dma1;dma2),
DeMorgan-algebra: DeMorganAlgebra,
compose: f o g,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dma-hom: dma-hom(dma1;dma2),
compose: f o g,
squash: ↓T,
prop: ℙ,
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2),
DeMorgan-algebra: DeMorganAlgebra,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
dma-neg_wf,
iff_weakening_equal,
uall_wf,
dma-hom_wf,
DeMorgan-algebra_wf,
compose-bounded-lattice-hom,
bdd-distributive-lattice-subtype-bdd-lattice,
DeMorgan-algebra-subtype,
subtype_rel_transitivity,
bdd-distributive-lattice_wf,
bdd-lattice_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
sqequalRule,
applyEquality,
lambdaEquality,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
axiomEquality,
dependent_functionElimination,
isect_memberEquality,
instantiate
Latex:
\mforall{}[dma1,dma2,dma3:DeMorganAlgebra]. \mforall{}[f:dma-hom(dma1;dma2)]. \mforall{}[g:dma-hom(dma2;dma3)].
(g o f \mmember{} dma-hom(dma1;dma3))
Date html generated:
2020_05_20-AM-08_56_12
Last ObjectModification:
2017_07_28-AM-09_17_17
Theory : lattices
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