Nuprl Lemma : fpf-join-ap-sq
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[f:a:A fp-> Top]. ∀[g:Top]. ∀[x:A]. (f ⊕ g(x) ~ if x ∈ dom(f) then f(x) else g(x) fi )
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t
Lemmas :
fpf-dom_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
top_wf,
fpf_wf,
deq_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f:a:A fp-> Top]. \mforall{}[g:Top]. \mforall{}[x:A].
(f \moplus{} g(x) \msim{} if x \mmember{} dom(f) then f(x) else g(x) fi )
Date html generated:
2015_07_17-AM-09_20_06
Last ObjectModification:
2015_01_28-AM-07_48_10
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