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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_commute
In [2]:
# check that the built expression is the same as the stored expression
assert rightward_commute.expr == stored_expr
assert rightward_commute.expr._style_id == stored_expr._style_id
print("Passed sanity check: rightward_commute matches stored_expr")
Passed sanity check: rightward_commute 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}~|~A_{1}, A_{2}, \ldots, A_{l}, B,C_{1}, C_{2}, \ldots, C_{m},D_{1}, D_{2}, \ldots, D_{n}}~\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)\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
3ExprTuple30, 32, 35
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 23
operands: 9
7Literal
8ExprTuple10
9ExprTuple11, 12, 13
10Lambdaparameters: 24
body: 14
11Operationoperator: 17
operands: 15
12Operationoperator: 17
operands: 16
13Operationoperator: 17
operands: 18
14Conditionalvalue: 19
condition: 20
15ExprTuple30, 21
16ExprTuple32, 21
17Literal
18ExprTuple35, 21
19Operationoperator: 23
operands: 22
20Operationoperator: 23
operands: 24
21Literal
22ExprTuple25, 27, 26, 28
23Literal
24ExprTuple25, 26, 27, 28
25ExprRangelambda_map: 29
start_index: 34
end_index: 30
26Variable
27ExprRangelambda_map: 31
start_index: 34
end_index: 32
28ExprRangelambda_map: 33
start_index: 34
end_index: 35
29Lambdaparameter: 43
body: 36
30Variable
31Lambdaparameter: 43
body: 37
32Variable
33Lambdaparameter: 43
body: 38
34Literal
35Variable
36IndexedVarvariable: 39
index: 43
37IndexedVarvariable: 40
index: 43
38IndexedVarvariable: 41
index: 43
39Variable
40Variable
41Variable
42ExprTuple43
43Variable