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Expression of type Equals

from the theory of proveit.numbers.division

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import x, y
from proveit.core_expr_types import w_1_to_m, z_1_to_n
from proveit.logic import Equals
from proveit.numbers import Mult, Neg, frac
In [2]:
# build up the expression from sub-expressions
expr = Equals(frac(x, Mult(w_1_to_m, Neg(y), z_1_to_n)), Neg(frac(x, Mult(w_1_to_m, y, z_1_to_n))))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\frac{x}{w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot \left(-y\right)\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}} = \left(-\frac{x}{w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot y\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}}\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 10
operands: 5
4Operationoperator: 15
operand: 8
5ExprTuple13, 7
6ExprTuple8
7Operationoperator: 17
operands: 9
8Operationoperator: 10
operands: 11
9ExprTuple19, 12, 21
10Literal
11ExprTuple13, 14
12Operationoperator: 15
operand: 20
13Variable
14Operationoperator: 17
operands: 18
15Literal
16ExprTuple20
17Literal
18ExprTuple19, 20, 21
19ExprRangelambda_map: 22
start_index: 25
end_index: 23
20Variable
21ExprRangelambda_map: 24
start_index: 25
end_index: 26
22Lambdaparameter: 32
body: 27
23Variable
24Lambdaparameter: 32
body: 28
25Literal
26Variable
27IndexedVarvariable: 29
index: 32
28IndexedVarvariable: 30
index: 32
29Variable
30Variable
31ExprTuple32
32Variable