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Theorem frac_cancel_left 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_left
In [2]:
# check that the built expression is the same as the stored expression
assert frac_cancel_left.expr == stored_expr
assert frac_cancel_left.expr._style_id == stored_expr._style_id
print("Passed sanity check: frac_cancel_left matches stored_expr")
Passed sanity check: frac_cancel_left 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{x \cdot y}{x \cdot z} = \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: 6
operand: 2
1ExprTuple2
2Lambdaparameters: 34
body: 3
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 10
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10
8Literal
9ExprTuple11, 12
10Lambdaparameter: 35
body: 14
11Operationoperator: 22
operands: 15
12Operationoperator: 22
operands: 16
13ExprTuple35
14Conditionalvalue: 17
condition: 18
15ExprTuple36, 19
16ExprTuple37, 19
17Operationoperator: 20
operands: 21
18Operationoperator: 22
operands: 23
19Literal
20Literal
21ExprTuple24, 25
22Literal
23ExprTuple35, 26
24Operationoperator: 28
operands: 27
25Operationoperator: 28
operands: 29
26Literal
27ExprTuple30, 31
28Literal
29ExprTuple35, 37
30Operationoperator: 33
operands: 32
31Operationoperator: 33
operands: 34
32ExprTuple36, 35
33Literal
34ExprTuple36, 37
35Variable
36Variable
37Variable