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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 rightward_commutation
In [2]:
# check that the built expression is the same as the stored expression
assert rightward_commutation.expr == stored_expr
assert rightward_commutation.expr._style_id == stored_expr._style_id
print("Passed sanity check: rightward_commutation matches stored_expr")
Passed sanity check: rightward_commutation 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, C_{1}, C_{2}, \ldots, C_{m}, D_{1}, D_{2}, \ldots, D_{n} \in \mathbb{B}}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l} \land B\land C_{1} \land  C_{2} \land  \ldots \land  C_{m}\land D_{1} \land  D_{2} \land  \ldots \land  D_{n}\right) =  \\ \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l}\land C_{1} \land  C_{2} \land  \ldots \land  C_{m} \land B\land D_{1} \land  D_{2} \land  \ldots \land  D_{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
3ExprTuple45, 47, 50
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 31
operands: 9
7Literal
8ExprTuple10
9ExprTuple11, 12, 13
10Lambdaparameters: 30
body: 14
11Operationoperator: 53
operands: 15
12Operationoperator: 53
operands: 16
13Operationoperator: 53
operands: 17
14Conditionalvalue: 18
condition: 19
15ExprTuple45, 20
16ExprTuple47, 20
17ExprTuple50, 20
18Operationoperator: 21
operands: 22
19Operationoperator: 31
operands: 23
20Literal
21Literal
22ExprTuple24, 25
23ExprTuple26, 27, 28, 29
24Operationoperator: 31
operands: 30
25Operationoperator: 31
operands: 32
26ExprRangelambda_map: 33
start_index: 49
end_index: 45
27Operationoperator: 53
operands: 34
28ExprRangelambda_map: 35
start_index: 49
end_index: 47
29ExprRangelambda_map: 36
start_index: 49
end_index: 50
30ExprTuple37, 41, 38, 39
31Literal
32ExprTuple37, 38, 41, 39
33Lambdaparameter: 63
body: 40
34ExprTuple41, 58
35Lambdaparameter: 63
body: 42
36Lambdaparameter: 63
body: 43
37ExprRangelambda_map: 44
start_index: 49
end_index: 45
38ExprRangelambda_map: 46
start_index: 49
end_index: 47
39ExprRangelambda_map: 48
start_index: 49
end_index: 50
40Operationoperator: 53
operands: 51
41Variable
42Operationoperator: 53
operands: 52
43Operationoperator: 53
operands: 54
44Lambdaparameter: 63
body: 55
45Variable
46Lambdaparameter: 63
body: 56
47Variable
48Lambdaparameter: 63
body: 57
49Literal
50Variable
51ExprTuple55, 58
52ExprTuple56, 58
53Literal
54ExprTuple57, 58
55IndexedVarvariable: 59
index: 63
56IndexedVarvariable: 60
index: 63
57IndexedVarvariable: 61
index: 63
58Literal
59Variable
60Variable
61Variable
62ExprTuple63
63Variable