Nuprl Lemma : set-sig-add-prop
∀[Item:Type]
∀s:set-sig{i:l}(Item). ∀set:set-sig-set(s). ∀x,y:Item.
(↑(set-sig-member(s) x (set-sig-add(s) y set)) ⇐⇒ (x = y ∈ Item) ∨ (↑(set-sig-member(s) x set)))
Proof
Definitions occuring in Statement :
set-sig-add: set-sig-add(s),
set-sig-member: set-sig-member(s),
set-sig-set: set-sig-set(s),
set-sig: set-sig{i:l}(Item),
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
apply: f a,
universe: Type,
equal: s = t ∈ T
Lemmas :
subtype_rel_self,
valueall-type_wf,
bool_wf,
all_wf,
not_wf,
assert_wf,
iff_wf,
equal_wf,
or_wf,
set_wf,
sq_stable__iff,
set-sig-member_wf,
set-sig-add_wf,
sq_stable__assert,
eqtt_to_assert,
squash_wf,
true_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
false_wf,
set-sig-set_wf,
set-sig_wf
\mforall{}[Item:Type]
\mforall{}s:set-sig\{i:l\}(Item). \mforall{}set:set-sig-set(s). \mforall{}x,y:Item.
(\muparrow{}(set-sig-member(s) x (set-sig-add(s) y set)) \mLeftarrow{}{}\mRightarrow{} (x = y) \mvee{} (\muparrow{}(set-sig-member(s) x set)))
Date html generated:
2015_07_17-AM-08_21_14
Last ObjectModification:
2015_04_02-PM-05_42_57
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