Nuprl Lemma : fpf-join-single-property
∀[A:Type]. ∀[B:A ─→ Type]. ∀[f:a:A fp-> B[a]]. ∀[a:A]. ∀[v:B[a]]. ∀[eq:EqDecider(A)]. ∀[b:A].
({(↑b ∈ dom(f)) ∧ (f ⊕ a : v(b) = f(b) ∈ B[b])}) supposing ((↑b ∈ dom(f ⊕ a : v)) and (¬(b = a ∈ A)))
Proof
Definitions occuring in Statement :
fpf-single: x : v,
fpf-join: f ⊕ g,
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
so_apply: x[s],
not: ¬A,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
fpf-join-dom,
fpf-single_wf,
fpf-single-dom,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
assert_wf,
fpf-join_wf,
not_wf,
equal_wf,
deq_wf,
fpf_wf,
assert_witness,
fpf-join-ap-sq,
bool_wf,
eqtt_to_assert,
fpf-ap_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[a:A]. \mforall{}[v:B[a]]. \mforall{}[eq:EqDecider(A)]. \mforall{}[b:A].
(\{(\muparrow{}b \mmember{} dom(f)) \mwedge{} (f \moplus{} a : v(b) = f(b))\}) supposing ((\muparrow{}b \mmember{} dom(f \moplus{} a : v)) and (\mneg{}(b = a)))
Date html generated:
2015_07_17-AM-11_12_49
Last ObjectModification:
2015_01_28-AM-07_41_50
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