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Expression of type Forall

from the theory of proveit.numbers.exponentiation

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 a
from proveit.core_expr_types import b_1_to_m
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Complex, Exp, RealPos
from proveit.numbers.exponentiation import prod_a_raise_bi__1_to_m
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b_1_to_m], instance_expr = Equals(prod_a_raise_bi__1_to_m, Exp(a, Add(b_1_to_m))), domains = [RealPos, 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 \in \mathbb{R}^+,\left(b_{1} \in \mathbb{C}\right), \left(b_{2} \in \mathbb{C}\right), \ldots, \left(b_{m} \in \mathbb{C}\right)}~\left(\left(a^{b_{1}} \cdot  a^{b_{2}} \cdot  \ldots \cdot  a^{b_{m}}\right) = a^{b_{1} +  b_{2} +  \ldots +  b_{m}}\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: 4
body: 5
4ExprTuple38, 31
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12, 13
10Literal
11ExprTuple14, 15
12Operationoperator: 16
operands: 17
13Operationoperator: 33
operands: 18
14Operationoperator: 28
operands: 19
15ExprRangelambda_map: 20
start_index: 36
end_index: 37
16Literal
17ExprTuple21
18ExprTuple38, 22
19ExprTuple38, 23
20Lambdaparameter: 42
body: 24
21ExprRangelambda_map: 25
start_index: 36
end_index: 37
22Operationoperator: 26
operands: 27
23Literal
24Operationoperator: 28
operands: 29
25Lambdaparameter: 42
body: 30
26Literal
27ExprTuple31
28Literal
29ExprTuple39, 32
30Operationoperator: 33
operands: 34
31ExprRangelambda_map: 35
start_index: 36
end_index: 37
32Literal
33Literal
34ExprTuple38, 39
35Lambdaparameter: 42
body: 39
36Literal
37Variable
38Variable
39IndexedVarvariable: 40
index: 42
40Variable
41ExprTuple42
42Variable