Nuprl Lemma : sg-pos-change-init
∀[g:SimpleGame]. ∀[j:Top]. (Pos(g@j) ~ {p:Pos(g)| sg-reachable(g;j;p)} )
Proof
Definitions occuring in Statement :
sg-change-init: g@j,
sg-reachable: sg-reachable(g;x;y),
sg-pos: Pos(g),
simple-game: SimpleGame,
uall: ∀[x:A]. B[x],
top: Top,
set: {x:A| B[x]} ,
sqequal: s ~ t
Definitions unfolded in proof :
pi1: fst(t),
spreadn: spread4,
sg-change-init: g@j,
sg-pos: Pos(g),
simple-game: SimpleGame,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
simple-game_wf,
top_wf
Rules used in proof :
because_Cache,
hypothesisEquality,
isectElimination,
isect_memberEquality,
extract_by_obid,
sqequalAxiom,
hypothesis,
sqequalRule,
thin,
productElimination,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g:SimpleGame]. \mforall{}[j:Top]. (Pos(g@j) \msim{} \{p:Pos(g)| sg-reachable(g;j;p)\} )
Date html generated:
2018_07_25-PM-01_35_11
Last ObjectModification:
2018_06_20-PM-03_47_50
Theory : co-recursion
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