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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.numbers.modular import interval_left_shift_bijection
In [2]:
# check that the built expression is the same as the stored expression
assert interval_left_shift_bijection.expr == stored_expr
assert interval_left_shift_bijection.expr._style_id == stored_expr._style_id
print("Passed sanity check: interval_left_shift_bijection matches stored_expr")
Passed sanity check: interval_left_shift_bijection 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_{a, b, c \in \mathbb{Z}}~\left(\left[x \mapsto \left(\left(c + x\right) ~\textup{mod}~ N\right)\right] \in \left[\{a~\ldotp \ldotp~b\} \xrightarrow[\text{onto}]{\text{1-to-1}} \{0~\ldotp \ldotp~N - 1\}\right]\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: 50
body: 4
3ExprTuple50
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 30
operands: 9
7Literal
8ExprTuple10
9ExprTuple50, 11
10Lambdaparameters: 12
body: 13
11Literal
12ExprTuple42, 43, 46
13Conditionalvalue: 14
condition: 15
14Operationoperator: 30
operands: 16
15Operationoperator: 17
operands: 18
16ExprTuple19, 20
17Literal
18ExprTuple21, 22, 23
19Lambdaparameter: 47
body: 25
20Operationoperator: 26
operands: 27
21Operationoperator: 30
operands: 28
22Operationoperator: 30
operands: 29
23Operationoperator: 30
operands: 31
24ExprTuple47
25Operationoperator: 32
operands: 33
26Literal
27ExprTuple34, 35
28ExprTuple42, 36
29ExprTuple43, 36
30Literal
31ExprTuple46, 36
32Literal
33ExprTuple37, 50
34Operationoperator: 39
operands: 38
35Operationoperator: 39
operands: 40
36Literal
37Operationoperator: 48
operands: 41
38ExprTuple42, 43
39Literal
40ExprTuple44, 45
41ExprTuple46, 47
42Variable
43Variable
44Literal
45Operationoperator: 48
operands: 49
46Variable
47Variable
48Literal
49ExprTuple50, 51
50Variable
51Operationoperator: 52
operand: 54
52Literal
53ExprTuple54
54Literal