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In [1]:
import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.logic.booleans.conjunction import disassociation
In [2]:
# check that the built expression is the same as the stored expression
assert disassociation.expr == stored_expr
assert disassociation.expr._style_id == stored_expr._style_id
print("Passed sanity check: disassociation matches stored_expr")
Passed sanity check: disassociation matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{l, m, n \in \mathbb{N}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n} \in \mathbb{B}}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l} \land \left(B_{1} \land  B_{2} \land  \ldots \land  B_{m}\right)\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) =  \\ \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l}\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) \end{array} \end{array}\right)\right]
In [4]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [5]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple43, 56, 45
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 40
operands: 9
7Literal
8ExprTuple10
9ExprTuple11, 12, 13
10Lambdaparameters: 30
body: 14
11Operationoperator: 48
operands: 15
12Operationoperator: 48
operands: 16
13Operationoperator: 48
operands: 17
14Conditionalvalue: 18
condition: 19
15ExprTuple43, 20
16ExprTuple56, 20
17ExprTuple45, 20
18Operationoperator: 21
operands: 22
19Operationoperator: 40
operands: 23
20Literal
21Literal
22ExprTuple24, 25
23ExprTuple26, 27, 28
24Operationoperator: 40
operands: 29
25Operationoperator: 40
operands: 30
26ExprRangelambda_map: 31
start_index: 55
end_index: 43
27ExprRangelambda_map: 32
start_index: 55
end_index: 56
28ExprRangelambda_map: 33
start_index: 55
end_index: 45
29ExprTuple35, 34, 36
30ExprTuple35, 50, 36
31Lambdaparameter: 62
body: 37
32Lambdaparameter: 62
body: 38
33Lambdaparameter: 62
body: 39
34Operationoperator: 40
operands: 41
35ExprRangelambda_map: 42
start_index: 55
end_index: 43
36ExprRangelambda_map: 44
start_index: 55
end_index: 45
37Operationoperator: 48
operands: 46
38Operationoperator: 48
operands: 47
39Operationoperator: 48
operands: 49
40Literal
41ExprTuple50
42Lambdaparameter: 62
body: 51
43Variable
44Lambdaparameter: 62
body: 52
45Variable
46ExprTuple51, 53
47ExprTuple59, 53
48Literal
49ExprTuple52, 53
50ExprRangelambda_map: 54
start_index: 55
end_index: 56
51IndexedVarvariable: 57
index: 62
52IndexedVarvariable: 58
index: 62
53Literal
54Lambdaparameter: 62
body: 59
55Literal
56Variable
57Variable
58Variable
59IndexedVarvariable: 60
index: 62
60Variable
61ExprTuple62
62Variable