Nuprl Lemma : fpf-compatible-triple
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[f,g,h:x:T fp-> Type].
({(g ⊆ h ⊕ f ⊕ g ∧ f ⊆ h ⊕ f ⊕ g) ∧ h ⊕ g ⊆ h ⊕ f ⊕ g ∧ h ⊕ f ⊆ h ⊕ f ⊕ g}) supposing (h || g and h || f and 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},
and: P ∧ Q,
universe: Type
Lemmas :
fpf-join-dom,
fpf-join_wf,
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
or_wf,
fpf-sub_witness,
fpf-compatible_wf,
fpf_wf,
deq_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
fpf-ap_wf,
fpf-join-ap-sq
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[f,g,h:x:T fp-> Type].
(\{(g \msubseteq{} h \moplus{} f \moplus{} g \mwedge{} f \msubseteq{} h \moplus{} f \moplus{} g) \mwedge{} h \moplus{} g \msubseteq{} h \moplus{} f \moplus{} g \mwedge{} h \moplus{} f \msubseteq{} h \moplus{} f \moplus{} g\}) supposing
(h || g and
h || f and
f || g)
Date html generated:
2015_07_17-AM-11_14_23
Last ObjectModification:
2015_01_28-AM-07_45_50
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