logo

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 a, b, c, d
from proveit.logic import Equals
from proveit.numbers import Add, Mult, frac, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Mult(Add(a, b, c), b)
expr = Equals(frac(sub_expr1, Mult(a, d)), Mult(frac(sub_expr1, d), frac(one, a)))
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{\left(a + b + c\right) \cdot b}{a \cdot d} = \left(\frac{\left(a + b + c\right) \cdot b}{d} \cdot \frac{1}{a}\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: 12
operands: 5
4Operationoperator: 17
operands: 6
5ExprTuple14, 7
6ExprTuple8, 9
7Operationoperator: 17
operands: 10
8Operationoperator: 12
operands: 11
9Operationoperator: 12
operands: 13
10ExprTuple22, 15
11ExprTuple14, 15
12Literal
13ExprTuple16, 22
14Operationoperator: 17
operands: 18
15Variable
16Literal
17Literal
18ExprTuple19, 23
19Operationoperator: 20
operands: 21
20Literal
21ExprTuple22, 23, 24
22Variable
23Variable
24Variable