Nuprl Lemma : sg-reachable_self
∀[g:SimpleGame]. ∀x:Pos(g). sg-reachable(g;x;x)
Proof
Definitions occuring in Statement :
sg-reachable: sg-reachable(g;x;y),
sg-pos: Pos(g),
simple-game: SimpleGame,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
sg-reachable: sg-reachable(g;x;y),
exists: ∃x:A. B[x],
member: t ∈ T,
seq-len: ||s||,
pi1: fst(t),
seq-cons: seq-cons(a;s),
seq-nil: seq-nil(),
and: P ∧ Q,
cand: A c∧ B,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
seq-item: s[i],
pi2: snd(t),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
btrue: tt,
subtract: n - m,
top: Top,
implies: P ⇒ Q,
nat: ℕ,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
prop: ℙ,
nat_plus: ℕ+,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q
Lemmas referenced :
seq-cons_wf,
sg-pos_wf,
seq-nil_wf,
add-commutes,
istype-void,
nat_properties,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermAdd_wf,
itermMultiply_wf,
itermConstant_wf,
itermVar_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
int_term_value_mul_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
istype-less_than,
istype-nat,
nat_plus_properties,
nat_plus_wf,
seq-len_wf,
seq-item_wf,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
decidable__lt,
istype-le,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
squash_wf,
sg-legal1_wf,
sg-legal2_wf,
simple-game_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
Error :dependent_pairFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_pairFormation,
natural_numberEquality,
imageMemberEquality,
baseClosed,
Error :isect_memberEquality_alt,
voidElimination,
setElimination,
rename,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
Error :universeIsType,
imageElimination,
addEquality,
multiplyEquality,
Error :productIsType,
applyEquality,
Error :inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
Error :equalityIstype,
because_Cache,
Error :dependent_set_memberEquality_alt,
unionElimination,
productElimination,
Error :functionIsType
Latex:
\mforall{}[g:SimpleGame]. \mforall{}x:Pos(g). sg-reachable(g;x;x)
Date html generated:
2019_06_20-PM-00_52_52
Last ObjectModification:
2019_01_02-PM-03_31_10
Theory : co-recursion-2
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