Nuprl Lemma : Sudoku-size_wf
∀[P:SudokuPuzzle()]. (Sudoku-size(P) ∈ ℕ)
Proof
Definitions occuring in Statement :
Sudoku-size: Sudoku-size(P),
SudokuPuzzle: SudokuPuzzle(),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Sudoku-size: Sudoku-size(P),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
ge: i ≥ j ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
non_neg_length,
non_neg_sum,
sudoku-allowed_wf,
int_seg_wf,
length_wf,
le_wf,
false_wf,
sum_wf,
SudokuPuzzle_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
dependent_set_memberEquality,
isectElimination,
thin,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
hypothesisEquality,
lambdaEquality,
because_Cache,
independent_isectElimination,
setElimination,
rename,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll
Latex:
\mforall{}[P:SudokuPuzzle()]. (Sudoku-size(P) \mmember{} \mBbbN{})
Date html generated:
2016_05_15-PM-03_14_14
Last ObjectModification:
2016_01_16-AM-10_47_49
Theory : general
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