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Theorem mod_real_closure 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_real_closure
In [2]:
# check that the built expression is the same as the stored expression
assert mod_real_closure.expr == stored_expr
assert mod_real_closure.expr._style_id == stored_expr._style_id
print("Passed sanity check: mod_real_closure matches stored_expr")
Passed sanity check: mod_real_closure 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}~|~b \neq 0}~\left(\left(a ~\textup{mod}~ b\right) \in \mathbb{R}\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: 15
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 17
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 22
8Literal
9ExprTuple11, 12, 13
10Operationoperator: 14
operands: 15
11Operationoperator: 17
operands: 16
12Operationoperator: 17
operands: 18
13Operationoperator: 19
operands: 20
14Literal
15ExprTuple21, 23
16ExprTuple21, 22
17Literal
18ExprTuple23, 22
19Literal
20ExprTuple23, 24
21Variable
22Literal
23Variable
24Literal