Nuprl Lemma : play-truncate_wf
∀[g:SimpleGame]. ∀[n:ℕ]. ∀[s:win2strat(g;n)]. ∀[f:strat2play(g;n;s)]. ∀[k:{(2 * n) + 2..||f|| + 1-}].
(play-truncate(f;k) ∈ {moves:strat2play(g;n;s)| ||moves|| = k ∈ ℤ} )
Proof
Definitions occuring in Statement :
strat2play: strat2play(g;n;s),
win2strat: win2strat(g;n),
play-truncate: play-truncate(f;m),
play-len: ||moves||,
simple-game: SimpleGame,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
int_seg: {i..j-},
prop: ℙ,
nat: ℕ,
guard: {T},
play-truncate: play-truncate(f;m),
play-len: ||moves||,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top
Lemmas referenced :
win2strat-strat2play-wf,
nat_wf,
simple-game_wf,
equal_wf,
play-len_wf,
int_seg_wf,
strat2play_subtype,
sequence_wf,
sg-pos_wf,
le_wf,
seq-len_wf,
subtype_rel_transitivity,
seq-len-truncate
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
setElimination,
rename,
addEquality,
multiplyEquality,
natural_numberEquality,
applyEquality,
lambdaEquality,
setEquality,
sqequalRule,
because_Cache,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[g:SimpleGame]. \mforall{}[n:\mBbbN{}]. \mforall{}[s:win2strat(g;n)]. \mforall{}[f:strat2play(g;n;s)].
\mforall{}[k:\{(2 * n) + 2..||f|| + 1\msupminus{}\}].
(play-truncate(f;k) \mmember{} \{moves:strat2play(g;n;s)| ||moves|| = k\} )
Date html generated:
2018_07_25-PM-01_32_34
Last ObjectModification:
2018_06_12-AM-10_03_54
Theory : co-recursion
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