Nuprl Lemma : sudoku-allowed_wf
∀[P:SudokuPuzzle()]. ∀[i,j:ℕ9]. (sudoku-allowed(P;i;j) ∈ {1..10-} List)
Proof
Definitions occuring in Statement :
sudoku-allowed: sudoku-allowed(P;i;j),
SudokuPuzzle: SudokuPuzzle(),
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sudoku-allowed: sudoku-allowed(P;i;j),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
SudokuPuzzle: SudokuPuzzle()
Lemmas referenced :
board-cell_wf,
list_wf,
int_seg_wf,
false_wf,
le_wf,
SudokuPuzzle_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
dependent_set_memberEquality,
independent_pairFormation,
lambdaFormation,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[P:SudokuPuzzle()]. \mforall{}[i,j:\mBbbN{}9]. (sudoku-allowed(P;i;j) \mmember{} \{1..10\msupminus{}\} List)
Date html generated:
2016_05_15-PM-03_14_11
Last ObjectModification:
2015_12_27-PM-01_02_08
Theory : general
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