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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
sub_expr1 = Mult(b, two)
sub_expr2 = Mult(b, three)
expr = Equals(Add(sub_expr1, sub_expr2, b, Neg(b)), Add(sub_expr1, sub_expr2, b, Mult(b, 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(b \cdot 2\right) + \left(b \cdot 3\right) + b - b\right) = \left(\left(b \cdot 2\right) + \left(b \cdot 3\right) + b + \left(b \cdot \left(-1\right)\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, 10, 19, 8
6Literal
7ExprTuple9, 10, 19, 11
8Operationoperator: 21
operand: 19
9Operationoperator: 15
operands: 13
10Operationoperator: 15
operands: 14
11Operationoperator: 15
operands: 16
12ExprTuple19
13ExprTuple19, 17
14ExprTuple19, 18
15Literal
16ExprTuple19, 20
17Literal
18Literal
19Variable
20Operationoperator: 21
operand: 23
21Literal
22ExprTuple23
23Literal