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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, b_1_to_j
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Complex, zero
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = Equals(Add(a_1_to_i, zero, b_1_to_j), Add(a_1_to_i, b_1_to_j)), domain = Complex)
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}, b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + 0+ b_{1} +  b_{2} +  \ldots +  b_{j}\right) = \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ b_{1} +  b_{2} +  \ldots +  b_{j}\right)\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: 17
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple13, 14
11Operationoperator: 16
operands: 15
12Operationoperator: 16
operands: 17
13ExprRangelambda_map: 18
start_index: 28
end_index: 26
14ExprRangelambda_map: 19
start_index: 28
end_index: 29
15ExprTuple21, 20, 22
16Literal
17ExprTuple21, 22
18Lambdaparameter: 39
body: 23
19Lambdaparameter: 39
body: 24
20Literal
21ExprRangelambda_map: 25
start_index: 28
end_index: 26
22ExprRangelambda_map: 27
start_index: 28
end_index: 29
23Operationoperator: 31
operands: 30
24Operationoperator: 31
operands: 32
25Lambdaparameter: 39
body: 33
26Variable
27Lambdaparameter: 39
body: 34
28Literal
29Variable
30ExprTuple33, 35
31Literal
32ExprTuple34, 35
33IndexedVarvariable: 36
index: 39
34IndexedVarvariable: 37
index: 39
35Literal
36Variable
37Variable
38ExprTuple39
39Variable