Nuprl Lemma : Game-add-Game0
∀G:Game. 0 ⊕ G ≡ G
Proof
Definitions occuring in Statement : 
eq-Game: G ≡ H
, 
Game-add: G ⊕ H
, 
Game0: 0
, 
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]
, 
Game-add: G ⊕ H
, 
left-indices: left-indices(g)
, 
pi1: fst(t)
, 
Game0: 0
, 
mk-Game: {L | R}
, 
mkGame: {mkGame(f[a] with a:L | g[b] with b:R}
, 
Wsup: Wsup(a;b)
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
and: P ∧ Q
, 
le: A ≤ B
, 
less_than: a < b
, 
squash: ↓T
, 
less_than': less_than'(a;b)
, 
length: ||as||
, 
list_ind: list_ind, 
nil: []
, 
it: ⋅
, 
right-indices: right-indices(g)
, 
pi2: snd(t)
, 
eq-Game: G ≡ H
, 
left-move: left-move(g;x)
, 
right-move: right-move(g;x)
, 
false: False
, 
uimplies: b supposing a
, 
not: ¬A
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
top: Top
, 
right-option: right-option{i:l}(g;m)
, 
left-option: left-option{i:l}(g;m)
, 
or: P ∨ Q
, 
guard: {T}
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
Game-induction, 
eq-Game_wf, 
Game-add_wf, 
Game0_wf, 
Game_wf, 
full-omega-unsat, 
intformand_wf, 
intformless_wf, 
itermVar_wf, 
itermConstant_wf, 
intformle_wf, 
int_formula_prop_and_lemma, 
int_formula_prop_less_lemma, 
int_term_value_var_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_le_lemma, 
int_formula_prop_wf, 
left-move_wf, 
equal_wf, 
exists_wf, 
right-indices_wf, 
right-move_wf, 
lelt_wf, 
left-indices_wf, 
all_wf, 
or_wf, 
left-option_wf, 
right-option_wf, 
eq-Game_inversion, 
subtype_rel_self
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isectElimination, 
thin, 
sqequalRule, 
lambdaEquality, 
cumulativity, 
hypothesis, 
hypothesisEquality, 
independent_functionElimination, 
lambdaFormation, 
independent_pairFormation, 
unionElimination, 
setElimination, 
rename, 
productElimination, 
natural_numberEquality, 
independent_isectElimination, 
approximateComputation, 
dependent_pairFormation, 
int_eqEquality, 
intEquality, 
dependent_functionElimination, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
inlFormation, 
because_Cache, 
instantiate, 
unionEquality, 
setEquality, 
inrFormation, 
functionEquality, 
inrEquality, 
equalityTransitivity, 
equalitySymmetry, 
applyEquality
Latex:
\mforall{}G:Game.  0  \moplus{}  G  \mequiv{}  G
Date html generated:
2019_10_31-AM-06_35_09
Last ObjectModification:
2018_08_21-PM-02_01_27
Theory : Numbers!and!Games
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