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Theorem mod_in_zero_set of type Forall

from the theory of proveit.numbers.modular

see dependencies

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 mod_in_zero_set
In [2]:
# check that the built expression is the same as the stored expression
assert mod_in_zero_set.expr == stored_expr
assert mod_in_zero_set.expr._style_id == stored_expr._style_id
print("Passed sanity check: mod_in_zero_set matches stored_expr")
Passed sanity check: mod_in_zero_set matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{a, b \in \mathbb{R}~|~a = 0}~\left(\left(a ~\textup{mod}~ b\right) \in \left\{0\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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 16
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 20
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple12, 13, 14
10Operationoperator: 15
operands: 16
11Operationoperator: 17
operand: 27
12Operationoperator: 20
operands: 19
13Operationoperator: 20
operands: 21
14Operationoperator: 22
operands: 23
15Literal
16ExprTuple26, 24
17Literal
18ExprTuple27
19ExprTuple26, 25
20Literal
21ExprTuple24, 25
22Literal
23ExprTuple26, 27
24Variable
25Literal
26Variable
27Literal