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Expression of type Equals

from the theory of proveit.numbers.summation

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 Conditional, Lambda, c, l
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Integer, Mult, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Add(l, one)
sub_expr2 = InSet(l, Integer)
expr = Equals(Lambda(l, Conditional(Mult(c, sub_expr1), sub_expr2)), Lambda(l, Conditional(Mult(sub_expr1, c), sub_expr2))).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[l \mapsto \left\{c \cdot \left(l + 1\right) \textrm{ if } l \in \mathbb{Z}\right..\right] =  \\ \left[l \mapsto \left\{\left(l + 1\right) \cdot c \textrm{ if } l \in \mathbb{Z}\right..\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
3Lambdaparameter: 21
body: 5
4Lambdaparameter: 21
body: 7
5Conditionalvalue: 8
condition: 10
6ExprTuple21
7Conditionalvalue: 9
condition: 10
8Operationoperator: 12
operands: 11
9Operationoperator: 12
operands: 13
10Operationoperator: 14
operands: 15
11ExprTuple17, 16
12Literal
13ExprTuple16, 17
14Literal
15ExprTuple21, 18
16Operationoperator: 19
operands: 20
17Variable
18Literal
19Literal
20ExprTuple21, 22
21Variable
22Literal