Nuprl Lemma : sg-pos-normalize
∀[g:SimpleGame]. (Pos(sg-normalize(g)) ~ {p:Pos(g)| sg-reachable(g;InitialPos(g);p)} )
Proof
Definitions occuring in Statement :
sg-normalize: sg-normalize(g),
sg-reachable: sg-reachable(g;x;y),
sg-init: InitialPos(g),
sg-pos: Pos(g),
simple-game: SimpleGame,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
sqequal: s ~ t
Definitions unfolded in proof :
top: Top,
member: t ∈ T,
uall: ∀[x:A]. B[x],
sg-normalize: sg-normalize(g)
Lemmas referenced :
simple-game_wf,
sg-pos-change-init
Rules used in proof :
sqequalAxiom,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[g:SimpleGame]. (Pos(sg-normalize(g)) \msim{} \{p:Pos(g)| sg-reachable(g;InitialPos(g);p)\} )
Date html generated:
2018_07_25-PM-01_35_14
Last ObjectModification:
2018_06_20-PM-03_48_14
Theory : co-recursion
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