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
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