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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