Nuprl Lemma : strat2play-add1
∀[g:SimpleGame]. ∀[n:ℕ]. ∀[s:win2strat(g;n)]. ∀[moves:strat2play(g;n;s)]. ∀[x:Pos(g)].
(seq-add(moves;x) ∈ strat2play(g;n;s))
Proof
Definitions occuring in Statement :
strat2play: strat2play(g;n;s),
win2strat: win2strat(g;n),
sg-pos: Pos(g),
simple-game: SimpleGame,
seq-add: seq-add(s;x),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
lelt: i ≤ j < k,
assert: ↑b,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
exists: ∃x:A. B[x],
bfalse: ff,
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
int_seg: {i..j-},
pi1: fst(t),
seq-truncate: seq-truncate(s;n),
seq-add: seq-add(s;x),
seq-len: ||s||,
sequence: sequence(T),
true: True,
less_than': less_than'(a;b),
subtract: n - m,
prop: ℙ,
false: False,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
not: ¬A,
iff: P ⇐⇒ Q,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
uiff: uiff(P;Q),
so_apply: x[s],
so_lambda: λ2x.t[x],
nat: ℕ,
le: A ≤ B,
top: Top,
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
int_seg_wf,
less_than_wf,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
assert_of_lt_int,
eqtt_to_assert,
bool_wf,
lt_int_wf,
sequence_wf,
le-add-cancel,
add-associates,
add-zero,
zero-mul,
add-mul-special,
add-commutes,
minus-one-mul-top,
add-swap,
minus-one-mul,
seq-len_wf,
minus-add,
condition-implies-le,
not-le-2,
false_wf,
decidable__le,
multiply-is-int-iff,
int_subtype_base,
le_wf,
set_subtype_base,
add-is-int-iff,
seq-add-len,
simple-game_wf,
nat_wf,
win2strat_wf,
strat2play_wf,
sg-pos_wf,
seq-add_wf,
strat2play_subtype,
strat2play-longer
Rules used in proof :
functionEquality,
cumulativity,
instantiate,
promote_hyp,
dependent_pairFormation,
equalityElimination,
functionExtensionality,
dependent_pairEquality,
multiplyEquality,
because_Cache,
minusEquality,
independent_functionElimination,
lambdaFormation,
independent_pairFormation,
unionElimination,
addEquality,
dependent_functionElimination,
natural_numberEquality,
lambdaEquality,
intEquality,
closedConclusion,
baseApply,
voidEquality,
voidElimination,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
productElimination,
independent_isectElimination,
imageElimination,
baseClosed,
imageMemberEquality,
rename,
setElimination,
applyLambdaEquality,
sqequalRule,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}[g:SimpleGame]. \mforall{}[n:\mBbbN{}]. \mforall{}[s:win2strat(g;n)]. \mforall{}[moves:strat2play(g;n;s)]. \mforall{}[x:Pos(g)].
(seq-add(moves;x) \mmember{} strat2play(g;n;s))
Date html generated:
2018_07_25-PM-01_33_27
Last ObjectModification:
2018_06_25-AM-10_53_07
Theory : co-recursion
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