Nuprl Lemma : mkGame_wf
∀[L,R:Type]. ∀[f:L ⟶ Game]. ∀[g:R ⟶ Game].  ({mkGame(f[a] with a:L | g[b] with b:R} ∈ Game)
Proof
Definitions occuring in Statement : 
mkGame: {mkGame(f[a] with a:L | g[b] with b:R}
, 
Game: Game
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
Game: Game
, 
mkGame: {mkGame(f[a] with a:L | g[b] with b:R}
, 
guard: {T}
, 
GameA: GameA{i:l}()
, 
subtype_rel: A ⊆r B
, 
GameB: GameB(p)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
Lemmas referenced : 
Wsup_wf, 
GameA_wf, 
GameB_wf, 
subtype_rel_self, 
equal_wf, 
Game_wf
Rules used in proof : 
cut, 
instantiate, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isectElimination, 
thin, 
hypothesis, 
sqequalRule, 
lambdaEquality, 
cumulativity, 
hypothesisEquality, 
isect_memberFormation, 
independent_pairEquality, 
applyEquality, 
unionEquality, 
equalityTransitivity, 
equalitySymmetry, 
lambdaFormation, 
unionElimination, 
dependent_functionElimination, 
independent_functionElimination, 
axiomEquality, 
functionEquality, 
isect_memberEquality, 
because_Cache, 
universeEquality
Latex:
\mforall{}[L,R:Type].  \mforall{}[f:L  {}\mrightarrow{}  Game].  \mforall{}[g:R  {}\mrightarrow{}  Game].    (\{mkGame(f[a]  with  a:L  |  g[b]  with  b:R\}  \mmember{}  Game)
Date html generated:
2019_10_31-AM-06_34_59
Last ObjectModification:
2018_08_21-PM-02_01_20
Theory : Numbers!and!Games
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