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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_axiom_expr # Load the stored axiom expression as 'stored_expr'
# import the special expression
from proveit.logic.sets.comprehension import comprehension_def
In [2]:
# check that the built expression is the same as the stored expression
assert comprehension_def.expr == stored_expr
assert comprehension_def.expr._style_id == stored_expr._style_id
print("Passed sanity check: comprehension_def matches stored_expr")
Passed sanity check: comprehension_def matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{n \in \mathbb{N}^+}~\left[\forall_{S_{1}, S_{2}, \ldots, S_{n}, Q, f, x}~\left(\begin{array}{c} \begin{array}{l} \left(x \in \left\{f\left(y_{1}, y_{2}, \ldots, y_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right\}_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)}\right) \\  = \left[\exists_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(x = f\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right)\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
2Lambdaparameter: 49
body: 4
3ExprTuple49
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 45
operands: 9
7Literal
8ExprTuple10
9ExprTuple49, 11
10Lambdaparameters: 12
body: 13
11Literal
12ExprTuple14, 41, 37, 33
13Operationoperator: 30
operands: 15
14ExprRangelambda_map: 16
start_index: 48
end_index: 49
15ExprTuple17, 18
16Lambdaparameter: 55
body: 50
17Operationoperator: 45
operands: 19
18Operationoperator: 20
operand: 23
19ExprTuple33, 22
20Literal
21ExprTuple23
22Operationoperator: 24
operand: 27
23Lambdaparameters: 42
body: 26
24Literal
25ExprTuple27
26Conditionalvalue: 28
condition: 32
27Lambdaparameters: 42
body: 29
28Operationoperator: 30
operands: 31
29Conditionalvalue: 34
condition: 32
30Literal
31ExprTuple33, 34
32Operationoperator: 35
operands: 36
33Variable
34Operationoperator: 37
operands: 42
35Literal
36ExprTuple38, 39
37Variable
38ExprRangelambda_map: 40
start_index: 48
end_index: 49
39Operationoperator: 41
operands: 42
40Lambdaparameter: 55
body: 43
41Variable
42ExprTuple44
43Operationoperator: 45
operands: 46
44ExprRangelambda_map: 47
start_index: 48
end_index: 49
45Literal
46ExprTuple51, 50
47Lambdaparameter: 55
body: 51
48Literal
49Variable
50IndexedVarvariable: 52
index: 55
51IndexedVarvariable: 53
index: 55
52Variable
53Variable
54ExprTuple55
55Variable