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
Home
Index