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Theorem int_mod_elimination 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 int_mod_elimination
In [2]:
# check that the built expression is the same as the stored expression
assert int_mod_elimination.expr == stored_expr
assert int_mod_elimination.expr._style_id == stored_expr._style_id
print("Passed sanity check: int_mod_elimination matches stored_expr")
Passed sanity check: int_mod_elimination matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{L \in \mathbb{N}^+}~\left[\forall_{x \in \{0~\ldotp \ldotp~L - 1\}}~\left(\left(x ~\textup{mod}~ L\right) = x\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: 31
body: 4
3ExprTuple31
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 18
operands: 9
7Literal
8ExprTuple10
9ExprTuple31, 11
10Lambdaparameter: 26
body: 13
11Literal
12ExprTuple26
13Conditionalvalue: 14
condition: 15
14Operationoperator: 16
operands: 17
15Operationoperator: 18
operands: 19
16Literal
17ExprTuple20, 26
18Literal
19ExprTuple26, 21
20Operationoperator: 22
operands: 23
21Operationoperator: 24
operands: 25
22Literal
23ExprTuple26, 31
24Literal
25ExprTuple27, 28
26Variable
27Literal
28Operationoperator: 29
operands: 30
29Literal
30ExprTuple31, 32
31Variable
32Operationoperator: 33
operand: 35
33Literal
34ExprTuple35
35Literal