Nuprl Lemma : subtype-fpf2
∀[A:Type]. ∀[B1,B2:A ─→ Type]. a:A fp-> B1[a] ⊆r a:A fp-> B2[a] supposing ∀a:A. (B1[a] ⊆r B2[a])
Proof
Definitions occuring in Statement :
fpf: a:A fp-> B[a],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
subtype_rel_product,
list_wf,
l_member_wf,
subtype_rel_dep_function,
set_wf,
all_wf,
subtype_rel_wf
\mforall{}[A:Type]. \mforall{}[B1,B2:A {}\mrightarrow{} Type]. a:A fp-> B1[a] \msubseteq{}r a:A fp-> B2[a] supposing \mforall{}a:A. (B1[a] \msubseteq{}r B2[a])
Date html generated:
2015_07_17-AM-09_15_29
Last ObjectModification:
2015_01_28-AM-07_53_06
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