Nuprl Lemma : right-move_wf
∀[g:Game]. ∀[x:right-indices(g)]. (right-move(g;x) ∈ Game)
Proof
Definitions occuring in Statement :
right-move: right-move(g;x),
right-indices: right-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}(),
right-move: right-move(g;x),
right-indices: right-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,
right-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,
inrEquality,
voidEquality,
because_Cache,
independent_isectElimination,
lambdaEquality,
voidElimination,
instantiate,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[g:Game]. \mforall{}[x:right-indices(g)]. (right-move(g;x) \mmember{} Game)
Date html generated:
2018_05_22-PM-09_52_32
Last ObjectModification:
2018_05_20-PM-10_36_50
Theory : Numbers!and!Games
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