Nuprl Lemma : fpf-compatible-join-iff
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ─→ Type]. ∀[f,g,h:a:A fp-> B[a]].
uiff(h || f ⊕ g;h || f ∧ h || g) supposing f || g
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-compatible: f || g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
fpf-compatible_wf,
fpf-join_wf,
fpf-compatible-join,
fpf_wf,
deq_wf,
fpf-join-dom,
fpf-join-ap-left,
iff_weakening_equal,
fpf-join-ap,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
eqff_to_assert,
assert_of_bnot
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f,g,h:a:A fp-> B[a]].
uiff(h || f \moplus{} g;h || f \mwedge{} h || g) supposing f || g
Date html generated:
2015_07_17-AM-11_12_13
Last ObjectModification:
2015_02_04-PM-05_06_51
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