Nuprl Lemma : left-move_wf
∀[g:Game]. ∀[x:left-indices(g)].  (left-move(g;x) ∈ Game)
Proof
Definitions occuring in Statement : 
left-move: left-move(g;x)
, 
left-indices: left-indices(g)
, 
Game: Game
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
subtype_rel: A ⊆r B
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
GameA: GameA{i:l}()
, 
left-move: left-move(g;x)
, 
left-indices: left-indices(g)
, 
pi1: fst(t)
, 
pi2: snd(t)
, 
GameB: GameB(p)
, 
uimplies: b supposing a
, 
prop: ℙ
Lemmas referenced : 
Game_subtype, 
GameA_wf, 
GameB_wf, 
Game_wf, 
subtype_rel_union, 
equal_wf, 
left-indices_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
thin, 
hypothesisEquality, 
applyEquality, 
extract_by_obid, 
hypothesis, 
sqequalHypSubstitution, 
sqequalRule, 
productEquality, 
functionEquality, 
cumulativity, 
isectElimination, 
lambdaFormation, 
productElimination, 
functionExtensionality, 
independent_pairEquality, 
inlEquality, 
voidEquality, 
because_Cache, 
independent_isectElimination, 
lambdaEquality, 
voidElimination, 
instantiate, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
independent_functionElimination, 
axiomEquality, 
isect_memberEquality
Latex:
\mforall{}[g:Game].  \mforall{}[x:left-indices(g)].    (left-move(g;x)  \mmember{}  Game)
Date html generated:
2018_05_22-PM-09_52_28
Last ObjectModification:
2018_05_20-PM-10_36_47
Theory : Numbers!and!Games
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