Nuprl Lemma : strat2play_subtype
∀[g:SimpleGame]. ∀[n:ℕ]. ∀[s:win2strat(g;n)].
  (strat2play(g;n;s) ⊆r {moves:sequence(Pos(g))| ((2 * n) + 2) ≤ ||moves||} )
Proof
Definitions occuring in Statement : 
strat2play: strat2play(g;n;s)
, 
win2strat: win2strat(g;n)
, 
sg-pos: Pos(g)
, 
simple-game: SimpleGame
, 
seq-len: ||s||
, 
sequence: sequence(T)
, 
nat: ℕ
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
le: A ≤ B
, 
set: {x:A| B[x]} 
, 
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
, 
strat2play: strat2play(g;n;s)
, 
nat: ℕ
, 
and: P ∧ Q
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
exists: ∃x:A. B[x]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
prop: ℙ
, 
le: A ≤ B
, 
top: Top
, 
subtract: n - m
, 
sq_type: SQType(T)
, 
guard: {T}
, 
ge: i ≥ j 
, 
squash: ↓T
, 
or: P ∨ Q
, 
uiff: uiff(P;Q)
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
iff: P 
⇐⇒ Q
, 
not: ¬A
, 
rev_implies: P 
⇐ Q
, 
bfalse: ff
Lemmas referenced : 
strat2play_wf, 
win2strat_wf, 
nat_wf, 
simple-game_wf, 
eq_int_wf, 
seq-len_wf, 
sg-pos_wf, 
set_subtype_base, 
le_wf, 
int_subtype_base, 
equal_wf, 
add-commutes, 
subtract_wf, 
minus-zero, 
zero-add, 
add-zero, 
subtype_base_sq, 
mul-commutes, 
assert_wf, 
bnot_wf, 
not_wf, 
equal-wf-T-base, 
bool_cases, 
bool_wf, 
bool_subtype_base, 
eqtt_to_assert, 
assert_of_eq_int, 
eqff_to_assert, 
iff_transitivity, 
iff_weakening_uiff, 
assert_of_bnot, 
nat_properties
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lambdaEquality, 
sqequalHypSubstitution, 
extract_by_obid, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
sqequalRule, 
axiomEquality, 
isect_memberEquality, 
because_Cache, 
setElimination, 
rename, 
natural_numberEquality, 
equalityTransitivity, 
equalitySymmetry, 
productElimination, 
lambdaFormation, 
dependent_pairFormation, 
sqequalIntensionalEquality, 
applyEquality, 
intEquality, 
independent_isectElimination, 
dependent_functionElimination, 
independent_functionElimination, 
promote_hyp, 
dependent_set_memberEquality, 
addEquality, 
multiplyEquality, 
voidElimination, 
voidEquality, 
instantiate, 
cumulativity, 
baseClosed, 
dependentIntersectionElimination, 
applyLambdaEquality, 
imageMemberEquality, 
imageElimination, 
unionElimination, 
independent_pairFormation, 
impliesFunctionality
Latex:
\mforall{}[g:SimpleGame].  \mforall{}[n:\mBbbN{}].  \mforall{}[s:win2strat(g;n)].
    (strat2play(g;n;s)  \msubseteq{}r  \{moves:sequence(Pos(g))|  ((2  *  n)  +  2)  \mleq{}  ||moves||\}  )
Date html generated:
2018_07_25-PM-01_32_25
Last ObjectModification:
2018_06_12-PM-01_15_15
Theory : co-recursion
Home
Index