Nuprl Lemma : pv11_p1_add_if_new_iff
∀Cmd:ValueAllType. ∀p,x:ℤ × Cmd. ∀proposals:(ℤ × Cmd) List.
((p ∈ pv11_p1_add_if_new() pv11_p1_same_proposal(Cmd) x proposals)
⇐⇒ (p ∈ proposals) ∨ if (∃z∈proposals.pv11_p1_same_proposal(Cmd) x z)_b then False else p = x ∈ (ℤ × Cmd) fi )
Proof
Definitions occuring in Statement :
pv11_p1_add_if_new: pv11_p1_add_if_new(),
pv11_p1_same_proposal: pv11_p1_same_proposal(Cmd),
bl-exists: (∃x∈L.P[x])_b,
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
ifthenelse: if b then t else f fi ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
false: False,
apply: f a,
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T
Lemmas :
bl-exists_wf,
l_member_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert-bl-exists,
false_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
assert-bnot,
l_exists_wf,
assert_wf,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
assert_of_bnot,
member_append,
cons_wf,
nil_wf,
member_singleton,
or_wf,
pv11_p1_add_if_new_wf,
list_wf,
pv11_p1_same_proposal_wf,
equal-wf-T-base,
iff_imp_equal_bool,
bfalse_wf,
iff_wf,
valueall-type_wf
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}p,x:\mBbbZ{} \mtimes{} Cmd. \mforall{}proposals:(\mBbbZ{} \mtimes{} Cmd) List.
((p \mmember{} pv11\_p1\_add\_if\_new() pv11\_p1\_same\_proposal(Cmd) x proposals)
\mLeftarrow{}{}\mRightarrow{} (p \mmember{} proposals)
\mvee{} if (\mexists{}z\mmember{}proposals.pv11\_p1\_same\_proposal(Cmd) x z)\_b then False else p = x fi )
Date html generated:
2015_07_23-PM-04_44_27
Last ObjectModification:
2015_01_29-AM-11_20_22
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