Nuprl Lemma : fpf-join-sub
∀[A:Type]. ∀[B:A ─→ Type]. ∀[eq:EqDecider(A)]. ∀[f1,g1,f2,g2:a:A fp-> B[a]].
(f1 ⊕ f2 ⊆ g1 ⊕ g2) supposing (f2 ⊆ g2 and f1 ⊆ g1 and f2 || g1)
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],
so_apply: x[s],
function: x:A ─→ B[x],
universe: Type
Lemmas :
fpf-join-dom,
assert_wf,
fpf-dom_wf,
fpf-join_wf,
top_wf,
subtype-fpf2,
subtype_top,
fpf-sub_witness,
fpf-sub_wf,
fpf-compatible_wf,
fpf_wf,
deq_wf,
equal-wf-T-base,
bnot_wf,
not_wf,
bool_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
fpf-join-ap-sq
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f1,g1,f2,g2:a:A fp-> B[a]].
(f1 \moplus{} f2 \msubseteq{} g1 \moplus{} g2) supposing (f2 \msubseteq{} g2 and f1 \msubseteq{} g1 and f2 || g1)
Date html generated:
2015_07_17-AM-09_20_40
Last ObjectModification:
2015_01_28-AM-07_49_13
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