Nuprl Lemma : distributive-lattice-cat_wf
BddDistributiveLattice ∈ SmallCategory'
Proof
Definitions occuring in Statement :
distributive-lattice-cat: BddDistributiveLattice,
small-category: SmallCategory,
member: t ∈ T
Definitions unfolded in proof :
distributive-lattice-cat: BddDistributiveLattice,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
bdd-distributive-lattice: BoundedDistributiveLattice,
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
so_apply: x[s1;s2;s3;s4;s5],
uimplies: b supposing a,
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
compose: f o g,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
mk-cat_wf,
bdd-distributive-lattice_wf,
bounded-lattice-hom_wf,
id-is-bounded-lattice-hom,
bdd-distributive-lattice-subtype-bdd-lattice,
compose-bounded-lattice-hom,
bounded-lattice-hom-equal,
equal_wf,
comp_assoc,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
setElimination,
rename,
because_Cache,
applyEquality,
cumulativity,
hypothesisEquality,
universeEquality,
independent_isectElimination,
lambdaFormation,
independent_pairFormation,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_functionElimination
Latex:
BddDistributiveLattice \mmember{} SmallCategory'
Date html generated:
2017_10_05-AM-00_51_33
Last ObjectModification:
2017_07_28-AM-09_20_30
Theory : small!categories
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