Nuprl Lemma : strong-subtype-set3
∀[A,B:Type]. ∀[P:A ⟶ ℙ]. strong-subtype({x:A| P[x]} ;B) supposing strong-subtype(A;B)
Proof
Definitions occuring in Statement :
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s],
true: True,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
strong-subtype-set,
true_wf,
strong-subtype-set2,
strong-subtype_witness,
strong-subtype_wf,
strong-subtype_transitivity,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
lambdaEquality,
lambdaFormation,
natural_numberEquality,
applyEquality,
because_Cache,
sqequalRule,
setEquality,
universeEquality,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
voidElimination,
voidEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. strong-subtype(\{x:A| P[x]\} ;B) supposing strong-subtype(A;B)
Date html generated:
2016_05_13-PM-04_11_17
Last ObjectModification:
2015_12_26-AM-11_21_24
Theory : subtype_1
Home
Index