Nuprl Lemma : subtype-fpf-variant
∀[A:Type]. ∀[P:A ⟶ ℙ]. ∀[B:A ⟶ 𝕌']. (a:{a:A| P[a]} fp-> B[a] ⊆r a:A fp-> B[a])
Proof
Definitions occuring in Statement :
fpf: a:A fp-> B[a],
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Lemmas referenced :
subtype-fpf-general
Rules used in proof :
cut,
instantiate,
introduction,
extract_by_obid,
hypothesis
Latex:
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. \mforall{}[B:A {}\mrightarrow{} \mBbbU{}']. (a:\{a:A| P[a]\} fp-> B[a] \msubseteq{}r a:A fp-> B[a])
Date html generated:
2020_05_20-AM-09_02_20
Last ObjectModification:
2020_01_24-PM-02_46_08
Theory : finite!partial!functions
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