Nuprl Lemma : simple-product_subtype_base
∀[A,B:Type].  ((A × B) ⊆r Base) supposing ((B ⊆r Base) and (A ⊆r Base))
Proof
Definitions occuring in Statement : 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
product: x:A × B[x]
, 
base: Base
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
product_subtype_base, 
subtype_rel_wf, 
base_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
sqequalRule, 
lambdaEquality, 
independent_isectElimination, 
hypothesis, 
lambdaFormation, 
because_Cache, 
axiomEquality, 
isect_memberEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality
Latex:
\mforall{}[A,B:Type].    ((A  \mtimes{}  B)  \msubseteq{}r  Base)  supposing  ((B  \msubseteq{}r  Base)  and  (A  \msubseteq{}r  Base))
Date html generated:
2016_05_13-PM-03_19_25
Last ObjectModification:
2015_12_26-AM-09_08_10
Theory : subtype_0
Home
Index