Nuprl Lemma : fpf-dom_functionality
∀[A:Type]. ∀[B:A ─→ Type]. ∀[eq1,eq2:EqDecider(A)]. ∀[f:a:A fp-> B[a]]. ∀[x:A]. x ∈ dom(f) = x ∈ dom(f)
Proof
Definitions occuring in Statement :
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
deq-member_wf,
bool_wf,
eqtt_to_assert,
assert-deq-member,
iff_imp_equal_bool,
btrue_wf,
true_wf,
l_member_wf,
assert_wf,
iff_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
bfalse_wf,
false_wf,
fpf_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq1,eq2:EqDecider(A)]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[x:A].
x \mmember{} dom(f) = x \mmember{} dom(f)
Date html generated:
2015_07_17-AM-09_15_53
Last ObjectModification:
2015_01_28-AM-07_52_52
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