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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 b
from proveit.core_expr_types import a_1_to_m
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, Exp, Mult, RealPos
from proveit.numbers.exponentiation import prod_ai_raise_b__1_to_m
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_m, b], instance_expr = Equals(Exp(Mult(a_1_to_m), b), prod_ai_raise_b__1_to_m), domains = [Complex, RealPos])
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_{\left(a_{1} \in \mathbb{C}\right), \left(a_{2} \in \mathbb{C}\right), \ldots, \left(a_{m} \in \mathbb{C}\right), b \in \mathbb{R}^+}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{m}\right)^{b} = \left(\left(a_{1}\right)^{b} \cdot  \left(a_{2}\right)^{b} \cdot  \ldots \cdot  \left(a_{m}\right)^{b}\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: 4
body: 5
4ExprTuple29, 38
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12, 13
10Literal
11ExprTuple14, 15
12Operationoperator: 35
operands: 16
13Operationoperator: 24
operands: 17
14ExprRangelambda_map: 18
start_index: 33
end_index: 34
15Operationoperator: 27
operands: 19
16ExprTuple20, 38
17ExprTuple21
18Lambdaparameter: 41
body: 22
19ExprTuple38, 23
20Operationoperator: 24
operands: 25
21ExprRangelambda_map: 26
start_index: 33
end_index: 34
22Operationoperator: 27
operands: 28
23Literal
24Literal
25ExprTuple29
26Lambdaparameter: 41
body: 30
27Literal
28ExprTuple37, 31
29ExprRangelambda_map: 32
start_index: 33
end_index: 34
30Operationoperator: 35
operands: 36
31Literal
32Lambdaparameter: 41
body: 37
33Literal
34Variable
35Literal
36ExprTuple37, 38
37IndexedVarvariable: 39
index: 41
38Variable
39Variable
40ExprTuple41
41Variable