Nuprl Lemma : Game-add_wf
∀[G,H:Game].  (G ⊕ H ∈ Game)
Proof
Definitions occuring in Statement : 
Game-add: G ⊕ H
, 
Game: Game
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
Game: Game
, 
all: ∀x:A. B[x]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
and: P ∧ Q
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
implies: P 
⇒ Q
, 
pcw-pp-barred: Barred(pp)
, 
nat: ℕ
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
ge: i ≥ j 
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
uimplies: b supposing a
, 
not: ¬A
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
top: Top
, 
cw-step: cw-step(A;a.B[a])
, 
pcw-step: pcw-step(P;p.A[p];p,a.B[p; a];p,a,b.C[p; a; b])
, 
spreadn: spread3, 
less_than: a < b
, 
less_than': less_than'(a;b)
, 
true: True
, 
squash: ↓T
, 
isr: isr(x)
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
btrue: tt
, 
ext-eq: A ≡ B
, 
unit: Unit
, 
it: ⋅
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
so_lambda: so_lambda(x,y,z.t[x; y; z])
, 
so_apply: x[s1;s2;s3]
, 
ext-family: F ≡ G
, 
pi1: fst(t)
, 
nat_plus: ℕ+
, 
W-rel: W-rel(A;a.B[a];w)
, 
param-W-rel: param-W-rel(P;p.A[p];p,a.B[p; a];p,a,b.C[p; a; b];par;w)
, 
pcw-steprel: StepRel(s1;s2)
, 
pi2: snd(t)
, 
isl: isl(x)
, 
pcw-step-agree: StepAgree(s;p1;w)
, 
cand: A c∧ B
, 
guard: {T}
, 
Wsup: Wsup(a;b)
, 
sq_type: SQType(T)
, 
le: A ≤ B
, 
sq_stable: SqStable(P)
, 
Game-add: G ⊕ H
, 
left-indices: left-indices(g)
, 
left-move: left-move(g;x)
, 
GameB: GameB(p)
, 
GameA: GameA{i:l}()
, 
right-indices: right-indices(g)
, 
right-move: right-move(g;x)
Lemmas referenced : 
Game_wf, 
W-elimination-facts, 
GameA_wf, 
GameB_wf, 
subtype_rel_self, 
int_seg_wf, 
subtract_wf, 
nat_properties, 
decidable__le, 
full-omega-unsat, 
intformand_wf, 
intformnot_wf, 
intformle_wf, 
itermConstant_wf, 
itermSubtract_wf, 
itermVar_wf, 
intformless_wf, 
int_formula_prop_and_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_le_lemma, 
int_term_value_constant_lemma, 
int_term_value_subtract_lemma, 
int_term_value_var_lemma, 
int_formula_prop_less_lemma, 
int_formula_prop_wf, 
decidable__lt, 
lelt_wf, 
top_wf, 
less_than_wf, 
false_wf, 
true_wf, 
equal_wf, 
add-subtract-cancel, 
itermAdd_wf, 
int_term_value_add_lemma, 
W-ext, 
param-co-W-ext, 
unit_wf2, 
it_wf, 
param-co-W_wf, 
pcw-steprel_wf, 
subtype_rel_dep_function, 
subtype_base_sq, 
nat_wf, 
set_subtype_base, 
le_wf, 
int_subtype_base, 
decidable__equal_int, 
intformeq_wf, 
int_formula_prop_eq_lemma, 
subtype_rel_function, 
int_seg_subtype, 
sq_stable__le, 
Wsup_wf, 
subtype_rel_union, 
mkGame_wf, 
left-indices_wf, 
right-indices_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
thin, 
sqequalHypSubstitution, 
dependent_functionElimination, 
hypothesisEquality, 
equalityTransitivity, 
hypothesis, 
equalitySymmetry, 
sqequalRule, 
axiomEquality, 
extract_by_obid, 
isect_memberEquality, 
isectElimination, 
because_Cache, 
instantiate, 
lambdaEquality, 
cumulativity, 
productElimination, 
strong_bar_Induction, 
applyEquality, 
universeEquality, 
independent_functionElimination, 
functionExtensionality, 
natural_numberEquality, 
setElimination, 
rename, 
dependent_set_memberEquality, 
independent_pairFormation, 
unionElimination, 
independent_isectElimination, 
approximateComputation, 
dependent_pairFormation, 
int_eqEquality, 
intEquality, 
voidElimination, 
voidEquality, 
lambdaFormation, 
lessCases, 
sqequalAxiom, 
imageMemberEquality, 
baseClosed, 
imageElimination, 
addEquality, 
int_eqReduceTrueSq, 
promote_hyp, 
hypothesis_subsumption, 
equalityElimination, 
dependent_pairEquality, 
inlEquality, 
unionEquality, 
productEquality, 
hyp_replacement, 
applyLambdaEquality, 
inrEquality
Latex:
\mforall{}[G,H:Game].    (G  \moplus{}  H  \mmember{}  Game)
Date html generated:
2018_05_22-PM-09_53_02
Last ObjectModification:
2018_05_20-PM-10_40_03
Theory : Numbers!and!Games
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