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Expression of type Conditional

from the theory of proveit.numbers.addition

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, IndexedVar, Variable, a, i
from proveit.core_expr_types import a_1_to_i
from proveit.logic import And, InSet
from proveit.numbers import Add, Natural, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(InSet(Add(a_1_to_i), Natural), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Natural), one, i)))
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(a_{1} +  a_{2} +  \ldots +  a_{i}\right) \in \mathbb{N} \textrm{ if } \left(a_{1} \in \mathbb{N}\right) \land  \left(a_{2} \in \mathbb{N}\right) \land  \ldots \land  \left(a_{i} \in \mathbb{N}\right)\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: 16
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 19
4Literal
5ExprTuple7
6Operationoperator: 8
operands: 9
7ExprRangelambda_map: 10
start_index: 14
end_index: 15
8Literal
9ExprTuple11
10Lambdaparameter: 22
body: 12
11ExprRangelambda_map: 13
start_index: 14
end_index: 15
12Operationoperator: 16
operands: 17
13Lambdaparameter: 22
body: 18
14Literal
15Variable
16Literal
17ExprTuple18, 19
18IndexedVarvariable: 20
index: 22
19Literal
20Variable
21ExprTuple22
22Variable