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
Definitions unfolded in proof :
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x]
Latex:
\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:
2016_05_16-AM-11_02_55
Last ObjectModification:
2015_12_29-AM-09_12_23
Theory : event-ordering
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