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
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