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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 n
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, five, four, frac, one, three, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = frac(two, five)
sub_expr2 = Exp(four, Add(one, n))
sub_expr3 = Exp(three, Add(n, one))
expr = Equals(Mult(sub_expr2, sub_expr3, sub_expr1), Mult(sub_expr1, sub_expr2, sub_expr3)).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(4^{1 + n} \cdot 3^{n + 1} \cdot \frac{2}{5}\right) =  \\ \left(\frac{2}{5} \cdot 4^{1 + n} \cdot 3^{n + 1}\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: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple9, 10, 8
6Literal
7ExprTuple8, 9, 10
8Operationoperator: 11
operands: 12
9Operationoperator: 14
operands: 13
10Operationoperator: 14
operands: 15
11Literal
12ExprTuple16, 17
13ExprTuple18, 19
14Literal
15ExprTuple20, 21
16Literal
17Literal
18Literal
19Operationoperator: 23
operands: 22
20Literal
21Operationoperator: 23
operands: 24
22ExprTuple26, 25
23Literal
24ExprTuple25, 26
25Variable
26Literal