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Expression of type Equals

from the theory of proveit.numbers.division

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, c
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, four, frac, one, three, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Neg(one)
expr = Equals(Mult(Mult(frac(four, three), a, b), Exp(Mult(frac(two, three), c), sub_expr1)), Mult(two, a, b, Exp(c, 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(\left(\frac{4}{3} \cdot a \cdot b\right) \cdot \left(\frac{2}{3} \cdot c\right)^{-1}\right) = \left(2 \cdot a \cdot b \cdot c^{-1}\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: 20
operands: 5
4Operationoperator: 20
operands: 6
5ExprTuple7, 8
6ExprTuple30, 15, 16, 9
7Operationoperator: 20
operands: 10
8Operationoperator: 12
operands: 11
9Operationoperator: 12
operands: 13
10ExprTuple14, 15, 16
11ExprTuple17, 18
12Literal
13ExprTuple26, 18
14Operationoperator: 28
operands: 19
15Variable
16Variable
17Operationoperator: 20
operands: 21
18Operationoperator: 22
operand: 27
19ExprTuple24, 31
20Literal
21ExprTuple25, 26
22Literal
23ExprTuple27
24Literal
25Operationoperator: 28
operands: 29
26Variable
27Literal
28Literal
29ExprTuple30, 31
30Literal
31Literal