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Expression of type Conditional

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 Conditional, ExprRange, Variable, n, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Complex, Mult, Natural, one
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(Add(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), x, one, n)), Mult(x, n)), And(InSet(n, Natural), InSet(x, Complex)))
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(x +  x +  ..\left(n - 3\right) \times.. +  x\right) = \left(x \cdot n\right) \textrm{ if } n \in \mathbb{N} ,  x \in \mathbb{C}\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple9, 10
7Operationoperator: 11
operands: 12
8Operationoperator: 13
operands: 14
9Operationoperator: 16
operands: 15
10Operationoperator: 16
operands: 17
11Literal
12ExprTuple18
13Literal
14ExprTuple25, 23
15ExprTuple23, 19
16Literal
17ExprTuple25, 20
18ExprRangelambda_map: 21
start_index: 22
end_index: 23
19Literal
20Literal
21Lambdaparameter: 26
body: 25
22Literal
23Variable
24ExprTuple26
25Variable
26Variable