Nuprl Lemma : type-lattice_wf
type-lattice{i:l}() ∈ bdd-lattice{i':l}
Proof
Definitions occuring in Statement :
type-lattice: type-lattice{i:l}(),
bdd-lattice: BoundedLattice,
member: t ∈ T
Definitions unfolded in proof :
type-lattice: type-lattice{i:l}(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
e-type: EType,
prop: ℙ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
and: P ∧ Q,
cand: A c∧ B,
quotient: x,y:A//B[x; y],
e-isect: e-isect(A;B),
all: ∀x:A. B[x],
implies: P ⇒ Q,
ext-eq: A ≡ B,
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
guard: {T},
bfalse: ff,
e-union: e-union(A;B),
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
pi2: snd(t),
top: Top
Lemmas referenced :
mk-bounded-lattice_wf,
e-type_wf,
e-isect_wf,
e-union_wf,
subtype_quotient,
ext-eq_wf,
istype-universe,
ext-eq-equiv,
top_wf,
quotient-member-eq,
isect2_wf,
isect2_decomp,
bool_wf,
b-union_wf,
bfalse_wf,
ifthenelse_wf,
btrue_wf,
istype-void
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality_alt,
hypothesisEquality,
inhabitedIsType,
universeIsType,
because_Cache,
universeEquality,
cumulativity,
independent_isectElimination,
closedConclusion,
voidEquality,
applyEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberFormation_alt,
pointwiseFunctionalityForEquality,
pertypeElimination,
promote_hyp,
productElimination,
dependent_functionElimination,
independent_functionElimination,
independent_pairFormation,
isect_memberEquality_alt,
unionElimination,
equalityElimination,
productIsType,
equalityIstype,
sqequalBase,
axiomEquality,
isectIsTypeImplies,
imageElimination,
imageMemberEquality,
dependent_pairEquality_alt,
baseClosed,
voidElimination
Latex:
type-lattice\{i:l\}() \mmember{} bdd-lattice\{i':l\}
Date html generated:
2020_05_20-AM-08_24_47
Last ObjectModification:
2019_12_08-PM-07_01_35
Theory : lattices
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