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Expression of type Forall

from the theory of proveit.linear_algebra.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 i
from proveit.core_expr_types import a_1_to_i
from proveit.linear_algebra import VecAdd
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Complex, NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [i], instance_expr = Forall(instance_param_or_params = [a_1_to_i], instance_expr = Equals(VecAdd(a_1_to_i), Add(a_1_to_i)), domain = Complex), domain = NaturalPos)
Out[2]:
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_{i \in \mathbb{N}^+}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i} \in \mathbb{C}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i}\right) = \left(a_{1} +  a_{2} +  \ldots +  a_{i}\right)\right)\right]
In [5]:
stored_expr.style_options()
Out[5]:
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()
Out[6]:
 core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 30
body: 4
3ExprTuple30
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 31
operands: 9
7Literal
8ExprTuple10
9ExprTuple30, 11
10Lambdaparameters: 24
body: 12
11Literal
12Conditionalvalue: 13
condition: 14
13Operationoperator: 15
operands: 16
14Operationoperator: 17
operands: 18
15Literal
16ExprTuple19, 20
17Literal
18ExprTuple21
19Operationoperator: 22
operands: 24
20Operationoperator: 23
operands: 24
21ExprRangelambda_map: 25
start_index: 29
end_index: 30
22Literal
23Literal
24ExprTuple26
25Lambdaparameter: 37
body: 27
26ExprRangelambda_map: 28
start_index: 29
end_index: 30
27Operationoperator: 31
operands: 32
28Lambdaparameter: 37
body: 33
29Literal
30Variable
31Literal
32ExprTuple33, 34
33IndexedVarvariable: 35
index: 37
34Literal
35Variable
36ExprTuple37
37Variable