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Expression of type Equals

from the theory of proveit.numbers.multiplication

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 a, b, c, d, x, y
from proveit.logic import Equals
from proveit.numbers import Mult, subtract
In [2]:
# build up the expression from sub-expressions
expr = Equals(Mult(a, d, subtract(x, y), b, c), subtract(Mult(a, d, x, b, c), Mult(a, d, y, b, c))).with_wrapping_at(2)
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())
\begin{array}{c} \begin{array}{l} \left(a \cdot d \cdot \left(x - y\right) \cdot b \cdot c\right) =  \\ \left(\left(a \cdot d \cdot x \cdot b \cdot c\right) - \left(a \cdot d \cdot y \cdot b \cdot c\right)\right) \end{array} \end{array}
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.()(2)('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: 19
operands: 5
4Operationoperator: 10
operands: 6
5ExprTuple21, 22, 7, 24, 25
6ExprTuple8, 9
7Operationoperator: 10
operands: 11
8Operationoperator: 19
operands: 12
9Operationoperator: 17
operand: 16
10Literal
11ExprTuple15, 14
12ExprTuple21, 22, 15, 24, 25
13ExprTuple16
14Operationoperator: 17
operand: 23
15Variable
16Operationoperator: 19
operands: 20
17Literal
18ExprTuple23
19Literal
20ExprTuple21, 22, 23, 24, 25
21Variable
22Variable
23Variable
24Variable
25Variable