Nuprl Lemma : shift-play_wf
∀[Pos:Type]. ∀[Mv:Pos ⟶ Type]. ∀[n:ℕ]. ∀[p:ℕn ⟶ MoveChoice(Pos;a.Mv[a])].
(shift-play(p) ∈ ℕn - 1 ⟶ MoveChoice(Pos;a.Mv[a]))
Proof
Definitions occuring in Statement :
shift-play: shift-play(p),
MoveChoice: MoveChoice(Pos;a.Mv[a]),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
subtract: n - m,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
shift-play: shift-play(p),
nat: ℕ,
int_seg: {i..j-},
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
lelt: i ≤ j < k,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
subtract: n - m,
prop: ℙ,
le: A ≤ B,
less_than: a < b,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
nat_wf,
MoveChoice_wf,
int_seg_wf,
lelt_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
itermSubtract_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
subtract_wf,
decidable__le,
nat_properties,
add-member-int_seg2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesis,
productElimination,
independent_isectElimination,
dependent_set_memberEquality,
independent_pairFormation,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[Pos:Type]. \mforall{}[Mv:Pos {}\mrightarrow{} Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[p:\mBbbN{}n {}\mrightarrow{} MoveChoice(Pos;a.Mv[a])].
(shift-play(p) \mmember{} \mBbbN{}n - 1 {}\mrightarrow{} MoveChoice(Pos;a.Mv[a]))
Date html generated:
2016_05_14-PM-03_56_44
Last ObjectModification:
2016_01_14-PM-09_43_37
Theory : spread
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