Nuprl Lemma : Game-add-assoc
∀G,H,K:Game.  G ⊕ H ⊕ K ≡ G ⊕ H ⊕ K
Proof
Definitions occuring in Statement : 
eq-Game: G ≡ H
, 
Game-add: G ⊕ H
, 
Game: Game
, 
all: ∀x:A. B[x]
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
member: t ∈ T
, 
prop: ℙ
, 
so_apply: x[s]
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
, 
eq-Game: G ≡ H
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
Game-add: G ⊕ H
, 
right-indices: right-indices(g)
, 
left-indices: left-indices(g)
, 
mkGame: {mkGame(f[a] with a:L | g[b] with b:R}
, 
Wsup: Wsup(a;b)
, 
pi1: fst(t)
, 
top: Top
, 
pi2: snd(t)
, 
guard: {T}
, 
exists: ∃x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
right-option: right-option{i:l}(g;m)
, 
left-option: left-option{i:l}(g;m)
, 
or: P ∨ Q
Lemmas referenced : 
Game-induction, 
all_wf, 
Game_wf, 
eq-Game_wf, 
Game-add_wf, 
left_move_add_inl_lemma, 
left_move_add_inr_lemma, 
left-indices_wf, 
right_move_add_inl_lemma, 
right_move_add_inr_lemma, 
right-indices_wf, 
or_wf, 
left-option_wf, 
right-option_wf, 
subtype_rel_union, 
left-move_wf, 
equal_wf, 
exists_wf, 
right-move_wf, 
eq-Game_inversion
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isectElimination, 
thin, 
sqequalRule, 
lambdaEquality, 
instantiate, 
hypothesis, 
cumulativity, 
hypothesisEquality, 
independent_functionElimination, 
lambdaFormation, 
independent_pairFormation, 
unionElimination, 
dependent_functionElimination, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
functionEquality, 
because_Cache, 
dependent_pairFormation, 
inlEquality, 
applyEquality, 
unionEquality, 
independent_isectElimination, 
inlFormation, 
inrEquality, 
inrFormation
Latex:
\mforall{}G,H,K:Game.    G  \moplus{}  H  \moplus{}  K  \mequiv{}  G  \moplus{}  H  \moplus{}  K
Date html generated:
2018_05_22-PM-09_53_38
Last ObjectModification:
2018_05_20-PM-10_41_43
Theory : Numbers!and!Games
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