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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, b, i, j
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import And, Forall, InSet
from proveit.numbers import Add, Less, Natural, RationalNeg, RationalNonPos, zero
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j], instance_expr = InSet(Add(a_1_to_i, b, c_1_to_j), RationalNeg), domain = RationalNonPos, condition = Less(b, zero)), And(InSet(i, Natural), InSet(j, 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}, b, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{Q}^{\leq 0}~|~b < 0}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) \in \mathbb{Q}^-\right) \textrm{ if } i \in \mathbb{N} ,  j \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: 16
operands: 5
3Literal
4ExprTuple6
5ExprTuple7, 8
6Lambdaparameters: 25
body: 9
7Operationoperator: 43
operands: 10
8Operationoperator: 43
operands: 11
9Conditionalvalue: 12
condition: 13
10ExprTuple38, 14
11ExprTuple41, 14
12Operationoperator: 43
operands: 15
13Operationoperator: 16
operands: 17
14Literal
15ExprTuple18, 19
16Literal
17ExprTuple20, 21, 22, 23
18Operationoperator: 24
operands: 25
19Literal
20ExprRangelambda_map: 26
start_index: 40
end_index: 38
21Operationoperator: 43
operands: 27
22ExprRangelambda_map: 28
start_index: 40
end_index: 41
23Operationoperator: 29
operands: 30
24Literal
25ExprTuple31, 35, 32
26Lambdaparameter: 51
body: 33
27ExprTuple35, 47
28Lambdaparameter: 51
body: 34
29Literal
30ExprTuple35, 36
31ExprRangelambda_map: 37
start_index: 40
end_index: 38
32ExprRangelambda_map: 39
start_index: 40
end_index: 41
33Operationoperator: 43
operands: 42
34Operationoperator: 43
operands: 44
35Variable
36Literal
37Lambdaparameter: 51
body: 45
38Variable
39Lambdaparameter: 51
body: 46
40Literal
41Variable
42ExprTuple45, 47
43Literal
44ExprTuple46, 47
45IndexedVarvariable: 48
index: 51
46IndexedVarvariable: 49
index: 51
47Literal
48Variable
49Variable
50ExprTuple51
51Variable