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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, i
from proveit.core_expr_types import a_1_to_i
from proveit.logic import Forall, InSet
from proveit.numbers import Add, IntegerNonPos, Natural
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i], instance_expr = InSet(Add(a_1_to_i), IntegerNonPos), domain = IntegerNonPos), InSet(i, Natural))
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\{\forall_{a_{1}, a_{2}, \ldots, a_{i} \in \mathbb{Z}^{\leq 0}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i}\right) \in \mathbb{Z}^{\leq 0}\right) \textrm{ if } i \in \mathbb{N}\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
operand: 6
2Operationoperator: 24
operands: 5
3Literal
4ExprTuple6
5ExprTuple23, 7
6Lambdaparameters: 17
body: 8
7Literal
8Conditionalvalue: 9
condition: 10
9Operationoperator: 24
operands: 11
10Operationoperator: 12
operands: 13
11ExprTuple14, 27
12Literal
13ExprTuple15
14Operationoperator: 16
operands: 17
15ExprRangelambda_map: 18
start_index: 22
end_index: 23
16Literal
17ExprTuple19
18Lambdaparameter: 30
body: 20
19ExprRangelambda_map: 21
start_index: 22
end_index: 23
20Operationoperator: 24
operands: 25
21Lambdaparameter: 30
body: 26
22Literal
23Variable
24Literal
25ExprTuple26, 27
26IndexedVarvariable: 28
index: 30
27Literal
28Variable
29ExprTuple30
30Variable