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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(one, five)
expr = Equals(Mult(four, Exp(three, n), Exp(four, n), two, three, sub_expr1), Mult(Exp(four, Add(one, n)), Exp(three, Add(n, one)), two, sub_expr1))
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(4 \cdot 3^{n} \cdot 4^{n} \cdot 2 \cdot 3 \cdot \frac{1}{5}\right) = \left(4^{1 + n} \cdot 3^{n + 1} \cdot 2 \cdot \frac{1}{5}\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
5ExprTuple21, 8, 9, 12, 23, 13
6Literal
7ExprTuple10, 11, 12, 13
8Operationoperator: 17
operands: 14
9Operationoperator: 17
operands: 15
10Operationoperator: 17
operands: 16
11Operationoperator: 17
operands: 18
12Literal
13Operationoperator: 19
operands: 20
14ExprTuple23, 29
15ExprTuple21, 29
16ExprTuple21, 22
17Literal
18ExprTuple23, 24
19Literal
20ExprTuple30, 25
21Literal
22Operationoperator: 27
operands: 26
23Literal
24Operationoperator: 27
operands: 28
25Literal
26ExprTuple30, 29
27Literal
28ExprTuple29, 30
29Variable
30Literal