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Expression of type Equals

from the theory of proveit.numbers.addition

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 b
from proveit.logic import Equals
from proveit.numbers import Add, Mult, Neg, one, three, two
In [2]:
# build up the expression from sub-expressions
expr = Equals(Add(Mult(two, b), Mult(three, b), b, Neg(b)), Mult(b, Add(two, three, one, Neg(one))))
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(2 \cdot b\right) + \left(3 \cdot b\right) + b - b\right) = \left(b \cdot \left(2 + 3 + 1 - 1\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: 15
operands: 5
4Operationoperator: 12
operands: 6
5ExprTuple7, 8, 17, 9
6ExprTuple17, 10
7Operationoperator: 12
operands: 11
8Operationoperator: 12
operands: 13
9Operationoperator: 21
operand: 17
10Operationoperator: 15
operands: 16
11ExprTuple18, 17
12Literal
13ExprTuple19, 17
14ExprTuple17
15Literal
16ExprTuple18, 19, 23, 20
17Variable
18Literal
19Literal
20Operationoperator: 21
operand: 23
21Literal
22ExprTuple23
23Literal