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Expression of type Forall

from the theory of proveit.numbers.integration

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 S
from proveit.core_expr_types import f__x_1_to_n, x_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import RealNonNeg
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = InSet(f__x_1_to_n, RealNonNeg), domain = S)
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_{x_{1}, x_{2}, \ldots, x_{n} \in S}~\left(f\left(x_{1}, x_{2}, \ldots, x_{n}\right) \in \mathbb{R}^{\ge 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: 14
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 21
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple12
10Operationoperator: 13
operands: 14
11Literal
12ExprRangelambda_map: 15
start_index: 19
end_index: 20
13Variable
14ExprTuple16
15Lambdaparameter: 27
body: 17
16ExprRangelambda_map: 18
start_index: 19
end_index: 20
17Operationoperator: 21
operands: 22
18Lambdaparameter: 27
body: 23
19Literal
20Variable
21Literal
22ExprTuple23, 24
23IndexedVarvariable: 25
index: 27
24Variable
25Variable
26ExprTuple27
27Variable