Nuprl Lemma : strat2play_subtype_le
∀[g:SimpleGame]. ∀[n:ℕ]. ∀[s:win2strat(g;n)]. ∀[j:ℕn + 1]. (strat2play(g;n;s) ⊆r strat2play(g;j;s))
Proof
Definitions occuring in Statement :
strat2play: strat2play(g;n;s),
win2strat: win2strat(g;n),
simple-game: SimpleGame,
int_seg: {i..j-},
nat: ℕ,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
bfalse: ff,
btrue: tt,
ifthenelse: if b then t else f fi ,
sq_type: SQType(T),
strat2play: strat2play(g;n;s),
top: Top,
true: True,
squash: ↓T,
subtract: n - m,
sq_stable: SqStable(P),
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
lelt: i ≤ j < k,
int_seg: {i..j-},
not: ¬A,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
guard: {T},
ge: i ≥ j ,
false: False,
implies: P ⇒ Q,
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
eqff_to_assert,
assert_of_eq_int,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases,
int_subtype_base,
equal-wf-base,
not_wf,
bnot_wf,
assert_wf,
le_weakening,
eq_int_wf,
lelt_wf,
simple-game_wf,
nat_wf,
not-lt-2,
zero-mul,
add-mul-special,
le_weakening2,
subtype_rel_transitivity,
decidable__lt,
minus-minus,
not-ge-2,
subtract_wf,
le_reflexive,
le-add-cancel,
add-zero,
not-equal-2,
decidable__int_equal,
le-add-cancel2,
add_functionality_wrt_le,
minus-zero,
add-commutes,
zero-add,
add-associates,
minus-one-mul-top,
add-swap,
minus-one-mul,
minus-add,
condition-implies-le,
less-iff-le,
sq_stable__le,
not-le-2,
decidable__le,
int_seg_subtype_nat,
win2strat_subtype,
le_wf,
false_wf,
strat2play_wf,
subtype_rel-equal,
win2strat_wf,
int_seg_wf,
less_than_wf,
ge_wf,
less_than_irreflexivity,
less_than_transitivity1,
nat_properties
Rules used in proof :
impliesFunctionality,
cumulativity,
instantiate,
dependentIntersectionElimination,
equalitySymmetry,
equalityTransitivity,
multiplyEquality,
intEquality,
voidEquality,
imageElimination,
baseClosed,
imageMemberEquality,
minusEquality,
because_Cache,
unionElimination,
applyEquality,
productElimination,
independent_pairFormation,
dependent_set_memberEquality,
addEquality,
axiomEquality,
isect_memberEquality,
dependent_functionElimination,
lambdaEquality,
sqequalRule,
voidElimination,
independent_functionElimination,
independent_isectElimination,
natural_numberEquality,
lambdaFormation,
intWeakElimination,
rename,
setElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g:SimpleGame]. \mforall{}[n:\mBbbN{}]. \mforall{}[s:win2strat(g;n)]. \mforall{}[j:\mBbbN{}n + 1]. (strat2play(g;n;s) \msubseteq{}r strat2play(g;j;s))
Date html generated:
2018_07_25-PM-01_32_29
Last ObjectModification:
2018_06_17-PM-09_31_39
Theory : co-recursion
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