Nuprl Lemma : W_sel_wf
∀[Pos:Type]
∀[Mv:Pos ⟶ Type]. ∀[n:ℕ]. ∀[w:WfdSpread(Pos;a.Mv[a])]. ∀[s:ℕn ⟶ MoveChoice(Pos;a.Mv[a])].
(W_sel(w;n;s) ∈ WfdSpread(Pos;a.Mv[a])?)
supposing ∀x,y:Pos. Dec(x = y ∈ Pos)
Proof
Definitions occuring in Statement :
W_sel: W_sel(w;n;s),
WfdSpread: WfdSpread(Pos;a.Mv[a]),
MoveChoice: MoveChoice(Pos;a.Mv[a]),
int_seg: {i..j-},
nat: ℕ,
decidable: Dec(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
W_sel: W_sel(w;n;s),
subgame: subgame(g;p;n),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
btrue: tt,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
guard: {T},
mkW: mkW(a;f),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
shift-play: shift-play(p),
nequal: a ≠ b ∈ T
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
int_seg_wf,
MoveChoice_wf,
WfdSpread_wf,
unit_wf2,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
WfdSpread-ext,
subtype_rel_weakening,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
mkW_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
shift-play_wf,
le_wf,
nat_wf,
all_wf,
decidable_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
applyEquality,
functionExtensionality,
inlEquality,
because_Cache,
unionElimination,
productEquality,
productElimination,
equalityElimination,
promote_hyp,
instantiate,
unionEquality,
dependent_set_memberEquality,
inrEquality,
universeEquality
Latex:
\mforall{}[Pos:Type]
\mforall{}[Mv:Pos {}\mrightarrow{} Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[w:WfdSpread(Pos;a.Mv[a])]. \mforall{}[s:\mBbbN{}n {}\mrightarrow{} MoveChoice(Pos;a.Mv[a])].
(W\_sel(w;n;s) \mmember{} WfdSpread(Pos;a.Mv[a])?)
supposing \mforall{}x,y:Pos. Dec(x = y)
Date html generated:
2017_04_17-AM-09_28_49
Last ObjectModification:
2017_02_27-PM-05_28_59
Theory : spread
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