Nuprl Lemma : e-isect_wf
∀[A,B:EType]. (e-isect(A;B) ∈ EType)
Proof
Definitions occuring in Statement :
e-isect: e-isect(A;B),
e-type: EType,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
e-type: EType,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
e-isect: e-isect(A;B),
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
prop: ℙ,
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
ext-eq: A ≡ B,
cand: A c∧ B,
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff
Lemmas referenced :
e-type_wf,
quotient-member-eq,
ext-eq_wf,
ext-eq-equiv,
isect2_wf,
isect2_decomp,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
introduction,
extract_by_obid,
hypothesis,
sqequalRule,
pertypeElimination,
productElimination,
thin,
instantiate,
isectElimination,
universeEquality,
lambdaEquality_alt,
hypothesisEquality,
applyEquality,
cumulativity,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
productIsType,
equalityIsType4,
because_Cache,
universeIsType,
independent_pairFormation,
isect_memberEquality,
unionElimination,
equalityElimination
Latex:
\mforall{}[A,B:EType]. (e-isect(A;B) \mmember{} EType)
Date html generated:
2020_05_20-AM-08_24_32
Last ObjectModification:
2018_10_12-PM-00_32_14
Theory : lattices
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