Nuprl Lemma : dep-isect-assoc
∀A:Type. ∀B:A ⟶ Type. ∀C:a:A ⟶ B[a] ⟶ Type. a:A ⋂ b:B[a] ⋂ C[a;b] ≡ z:a:A ⋂ B[a] ⋂ C[z;z]
Proof
Definitions occuring in Statement :
dep-isect: x:A ⋂ B[x],
ext-eq: A ≡ B,
so_apply: x[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_apply: x[s],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
guard: {T}
Lemmas referenced :
istype-universe,
dep-isect-subtype,
dep-isect_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
independent_pairFormation,
Error :lambdaEquality_alt,
Error :functionIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :universeIsType,
applyEquality,
Error :inhabitedIsType,
universeEquality,
equalitySymmetry,
equalityTransitivity,
dependentIntersectionEqElimination,
dependentIntersection_memberEquality,
dependentIntersectionElimination,
Error :depIsectIsType,
lambdaEquality,
sqequalRule,
dependent_functionElimination,
cumulativity
Latex:
\mforall{}A:Type. \mforall{}B:A {}\mrightarrow{} Type. \mforall{}C:a:A {}\mrightarrow{} B[a] {}\mrightarrow{} Type. a:A \mcap{} b:B[a] \mcap{} C[a;b] \mequiv{} z:a:A \mcap{} B[a] \mcap{} C[z;z]
Date html generated:
2019_06_20-PM-00_35_03
Last ObjectModification:
2018_10_08-PM-05_28_39
Theory : dependent!intersection
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