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Theorem mult_frac_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 mult_frac_right
In [2]:
# check that the built expression is the same as the stored expression
assert mult_frac_right.expr == stored_expr
assert mult_frac_right.expr._style_id == stored_expr._style_id
print("Passed sanity check: mult_frac_right matches stored_expr")
Passed sanity check: mult_frac_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, y, z \in \mathbb{C}~|~z \neq 0}~\left(\left(x \cdot \frac{y}{z}\right) = \frac{x \cdot y}{z}\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: 4
body: 5
4ExprTuple35, 36, 34
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12, 13
10Literal
11ExprTuple14, 15, 16, 17
12Operationoperator: 32
operands: 18
13Operationoperator: 30
operands: 19
14Operationoperator: 22
operands: 20
15Operationoperator: 22
operands: 21
16Operationoperator: 22
operands: 23
17Operationoperator: 24
operands: 25
18ExprTuple35, 26
19ExprTuple27, 34
20ExprTuple35, 28
21ExprTuple36, 28
22Literal
23ExprTuple34, 28
24Literal
25ExprTuple34, 29
26Operationoperator: 30
operands: 31
27Operationoperator: 32
operands: 33
28Literal
29Literal
30Literal
31ExprTuple36, 34
32Literal
33ExprTuple35, 36
34Variable
35Variable
36Variable