Nuprl Lemma : strong-subtype-set2
∀[A:Type]. ∀[P:A ⟶ ℙ]. strong-subtype({x:A| P[x]} ;A)
Proof
Definitions occuring in Statement :
strong-subtype: strong-subtype(A;B),
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,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
subtype_rel: A ⊆r B,
so_apply: x[s],
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q
Lemmas referenced :
and_wf,
equal_wf,
exists_wf,
strong-subtype_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
setElimination,
thin,
rename,
hypothesisEquality,
setEquality,
cumulativity,
applyEquality,
functionExtensionality,
hypothesis,
because_Cache,
sqequalHypSubstitution,
sqequalRule,
independent_pairFormation,
productElimination,
dependent_set_memberEquality,
equalitySymmetry,
extract_by_obid,
isectElimination,
hyp_replacement,
Error :applyLambdaEquality,
universeEquality,
independent_functionElimination,
functionEquality,
isect_memberEquality
Latex:
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. strong-subtype(\{x:A| P[x]\} ;A)
Date html generated:
2016_10_21-AM-09_41_30
Last ObjectModification:
2016_07_12-AM-05_03_32
Theory : subtype_1
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