Nuprl Lemma : dep-isect-subtype
∀A:Type. ∀B:A ⟶ Type. (x:A ⋂ B[x] ⊆r A)
Proof
Definitions occuring in Statement :
dep-isect: x:A ⋂ B[x],
subtype_rel: A ⊆r B,
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],
subtype_rel: A ⊆r B,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
dep-isect_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
lambdaEquality,
dependentIntersectionElimination,
sqequalHypSubstitution,
equalityTransitivity,
hypothesis,
equalitySymmetry,
cut,
lemma_by_obid,
dependent_functionElimination,
thin,
cumulativity,
hypothesisEquality,
sqequalRule,
applyEquality,
functionEquality,
universeEquality
Latex:
\mforall{}A:Type. \mforall{}B:A {}\mrightarrow{} Type. (x:A \mcap{} B[x] \msubseteq{}r A)
Date html generated:
2018_07_25-PM-01_30_17
Last ObjectModification:
2018_06_09-PM-09_18_11
Theory : dependent!intersection
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