Nuprl Lemma : play-item_wf
∀[g:SimpleGame]. ∀[n:ℕ]. ∀[s:win2strat(g;n)]. ∀[moves:strat2play(g;n;s)]. ∀[i:ℕ(2 * n) + 2]. (moves[i] ∈ Pos(g))
Proof
Definitions occuring in Statement :
strat2play: strat2play(g;n;s),
win2strat: win2strat(g;n),
play-item: moves[i],
sg-pos: Pos(g),
simple-game: SimpleGame,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
multiply: n * m,
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
nat: ℕ,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
play-item: moves[i],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
uimplies: b supposing a,
uiff: uiff(P;Q),
guard: {T}
Lemmas referenced :
strat2play_subtype,
set_wf,
sequence_wf,
sg-pos_wf,
le_wf,
seq-len_wf,
nat_wf,
seq-item_wf,
add-is-int-iff,
set_subtype_base,
int_subtype_base,
multiply-is-int-iff,
less_than_transitivity1,
lelt_wf,
equal_wf,
int_seg_wf,
strat2play_wf,
win2strat_wf,
simple-game_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
lambdaEquality,
addEquality,
multiplyEquality,
natural_numberEquality,
setElimination,
rename,
because_Cache,
lambdaFormation,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
baseApply,
closedConclusion,
baseClosed,
intEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[g:SimpleGame]. \mforall{}[n:\mBbbN{}]. \mforall{}[s:win2strat(g;n)]. \mforall{}[moves:strat2play(g;n;s)]. \mforall{}[i:\mBbbN{}(2 * n) + 2].
(moves[i] \mmember{} Pos(g))
Date html generated:
2018_07_25-PM-01_32_41
Last ObjectModification:
2018_06_11-PM-10_13_05
Theory : co-recursion
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