Nuprl Lemma : subtype-fpf3
∀[A1,A2:Type]. ∀[B1:A1 ─→ Type]. ∀[B2:A2 ─→ Type].
(a:A1 fp-> B1[a] ⊆r a:A2 fp-> B2[a]) supposing ((∀a:A1. (B1[a] ⊆r B2[a])) and strong-subtype(A1;A2))
Proof
Definitions occuring in Statement :
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
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 :
strong-subtype-implies,
subtype_rel_list,
l_member_wf,
fpf_wf,
all_wf,
subtype_rel_wf,
strong-subtype_wf,
strong-subtype-l_member-type,
strong-subtype-l_member
\mforall{}[A1,A2:Type]. \mforall{}[B1:A1 {}\mrightarrow{} Type]. \mforall{}[B2:A2 {}\mrightarrow{} Type].
(a:A1 fp-> B1[a] \msubseteq{}r a:A2 fp-> B2[a]) supposing
((\mforall{}a:A1. (B1[a] \msubseteq{}r B2[a])) and
strong-subtype(A1;A2))
Date html generated:
2015_07_17-AM-09_15_30
Last ObjectModification:
2015_01_28-AM-07_54_24
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