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Expression of type Equals

from the theory of proveit.numbers.exponentiation

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 a, b, n
from proveit.logic import Equals
from proveit.numbers import Exp, Neg, frac
In [2]:
# build up the expression from sub-expressions
expr = Equals(Exp(frac(a, b), Neg(n)), frac(Exp(b, n), Exp(a, n)))
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(\frac{a}{b}\right)^{-n} = \frac{b^{n}}{a^{n}}
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: 16
operands: 5
4Operationoperator: 11
operands: 6
5ExprTuple7, 8
6ExprTuple9, 10
7Operationoperator: 11
operands: 12
8Operationoperator: 13
operand: 20
9Operationoperator: 16
operands: 15
10Operationoperator: 16
operands: 17
11Literal
12ExprTuple19, 18
13Literal
14ExprTuple20
15ExprTuple18, 20
16Literal
17ExprTuple19, 20
18Variable
19Variable
20Variable