Nuprl Lemma : win2strat_subtype
∀[g:SimpleGame]. ∀[n,m:ℕ]. win2strat(g;n) ⊆r win2strat(g;m) supposing m ≤ n
Proof
Definitions occuring in Statement :
win2strat: win2strat(g;n),
simple-game: SimpleGame,
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
le: A ≤ B
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
squash: ↓T,
all: ∀x:A. B[x],
true: True,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
top: Top,
nat_plus: ℕ+,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T)
Lemmas referenced :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
le_wf,
subtype_rel-equal,
win2strat_wf,
false_wf,
le_antisymmetry,
le_reflexive,
decidable__le,
subtract_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-one-mul-top,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__lt,
nat_wf,
simple-game_wf,
subtype_rel_transitivity,
le_weakening2,
not-le-2,
win2strat-properties,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
decidable__int_equal,
not-equal-2,
not-lt-2,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
dependent_set_memberEquality,
independent_pairFormation,
applyEquality,
imageElimination,
productElimination,
imageMemberEquality,
baseClosed,
unionElimination,
addEquality,
voidEquality,
intEquality,
minusEquality,
instantiate,
cumulativity
Latex:
\mforall{}[g:SimpleGame]. \mforall{}[n,m:\mBbbN{}]. win2strat(g;n) \msubseteq{}r win2strat(g;m) supposing m \mleq{} n
Date html generated:
2018_07_25-PM-01_32_21
Last ObjectModification:
2018_06_13-AM-10_58_55
Theory : co-recursion
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