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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.logic import Equals
from proveit.numbers import Mult, Neg, five, frac, six, three, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Neg(frac(two, three))
expr = Equals(Mult(sub_expr1, frac(six, Neg(five))), Mult(sub_expr1, Neg(frac(six, five))))
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())
\left(\left(-\frac{2}{3}\right) \cdot \frac{6}{-5}\right) = \left(\left(-\frac{2}{3}\right) \cdot \left(-\frac{6}{5}\right)\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: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple9, 8
6Literal
7ExprTuple9, 10
8Operationoperator: 20
operands: 11
9Operationoperator: 17
operand: 15
10Operationoperator: 17
operand: 16
11ExprTuple24, 14
12ExprTuple15
13ExprTuple16
14Operationoperator: 17
operand: 25
15Operationoperator: 20
operands: 19
16Operationoperator: 20
operands: 21
17Literal
18ExprTuple25
19ExprTuple22, 23
20Literal
21ExprTuple24, 25
22Literal
23Literal
24Literal
25Literal