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Expression of type Forall

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.core_expr_types import a_1_to_i
from proveit.logic import Forall, InSet
from proveit.numbers import Add, RealNonPos
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i], instance_expr = InSet(Add(a_1_to_i), RealNonPos), domain = RealNonPos)
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())
\forall_{a_{1}, a_{2}, \ldots, a_{i} \in \mathbb{R}^{\le 0}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i}\right) \in \mathbb{R}^{\le 0}\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 13
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 20
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 23
8Literal
9ExprTuple11
10Operationoperator: 12
operands: 13
11ExprRangelambda_map: 14
start_index: 18
end_index: 19
12Literal
13ExprTuple15
14Lambdaparameter: 26
body: 16
15ExprRangelambda_map: 17
start_index: 18
end_index: 19
16Operationoperator: 20
operands: 21
17Lambdaparameter: 26
body: 22
18Literal
19Variable
20Literal
21ExprTuple22, 23
22IndexedVarvariable: 24
index: 26
23Literal
24Variable
25ExprTuple26
26Variable