Nuprl Lemma : fpf-sub-join
∀[A:Type]. ∀[B:A ─→ Type]. ∀[eq:EqDecider(A)]. ∀[f,g:a:A fp-> B[a]]. {f ⊆ f ⊕ g ∧ g ⊆ f ⊕ g} supposing f || g
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-compatible: f || g,
fpf-sub: f ⊆ g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
so_apply: x[s],
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
fpf-sub-join-left,
subtype-fpf2,
top_wf,
subtype_top,
fpf-sub-join-right,
fpf-sub_witness,
fpf-join_wf,
fpf-compatible_wf,
fpf_wf,
deq_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:A fp-> B[a]].
\{f \msubseteq{} f \moplus{} g \mwedge{} g \msubseteq{} f \moplus{} g\} supposing f || g
Date html generated:
2015_07_17-AM-09_20_37
Last ObjectModification:
2015_01_28-AM-07_47_34
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