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Theorem frac_cancel_right of type Forall

from the theory of proveit.numbers.division

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.division import frac_cancel_right
In [2]:
# check that the built expression is the same as the stored expression
assert frac_cancel_right.expr == stored_expr
assert frac_cancel_right.expr._style_id == stored_expr._style_id
print("Passed sanity check: frac_cancel_right matches stored_expr")
Passed sanity check: frac_cancel_right matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{x, z \in \mathbb{C}^{\neq 0}}~\left[\forall_{y \in \mathbb{C}}~\left(\frac{y \cdot x}{z \cdot x} = \frac{y}{z}\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
2Lambdaparameters: 3
body: 4
3ExprTuple38, 37
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple12, 13
11Lambdaparameter: 36
body: 15
12Operationoperator: 23
operands: 16
13Operationoperator: 23
operands: 17
14ExprTuple36
15Conditionalvalue: 18
condition: 19
16ExprTuple38, 20
17ExprTuple37, 20
18Operationoperator: 21
operands: 22
19Operationoperator: 23
operands: 24
20Literal
21Literal
22ExprTuple25, 26
23Literal
24ExprTuple36, 27
25Operationoperator: 29
operands: 28
26Operationoperator: 29
operands: 30
27Literal
28ExprTuple31, 32
29Literal
30ExprTuple36, 37
31Operationoperator: 34
operands: 33
32Operationoperator: 34
operands: 35
33ExprTuple36, 38
34Literal
35ExprTuple37, 38
36Variable
37Variable
38Variable