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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 a, b, c, d
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, four, frac, one, sqrt, three, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = frac(four, three)
sub_expr2 = Exp(d, two)
sub_expr3 = sqrt(b)
expr = Equals(Mult(Mult(sub_expr1, sub_expr2, b, a, c), Exp(sub_expr3, Neg(one))), Mult(sub_expr1, sub_expr2, sub_expr3, a, c))
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 d^{2} \cdot b \cdot a \cdot c\right) \cdot (\sqrt{b})^{-1}\right) = \left(\frac{4}{3} \cdot d^{2} \cdot \sqrt{b} \cdot a \cdot c\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: 9
operands: 5
4Operationoperator: 9
operands: 6
5ExprTuple7, 8
6ExprTuple12, 13, 16, 14, 15
7Operationoperator: 9
operands: 10
8Operationoperator: 20
operands: 11
9Literal
10ExprTuple12, 13, 27, 14, 15
11ExprTuple16, 17
12Operationoperator: 29
operands: 18
13Operationoperator: 20
operands: 19
14Variable
15Variable
16Operationoperator: 20
operands: 21
17Operationoperator: 22
operand: 31
18ExprTuple24, 25
19ExprTuple26, 32
20Literal
21ExprTuple27, 28
22Literal
23ExprTuple31
24Literal
25Literal
26Variable
27Variable
28Operationoperator: 29
operands: 30
29Literal
30ExprTuple31, 32
31Literal
32Literal