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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 ExprRange, IndexedVar, Variable, a, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, Mult, one, sqrt
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [a_1_to_n], instance_expr = Equals(sqrt(Mult(a_1_to_n)), Mult(ExprRange(sub_expr1, sqrt(IndexedVar(a, sub_expr1)), one, n))), 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_{n} \in \mathbb{C}}~\left(\sqrt{\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right)} = \left(\sqrt{\left(a_{1}\right)} \cdot  \sqrt{\left(a_{2}\right)} \cdot  \ldots \cdot  \sqrt{\left(a_{n}\right)}\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: 21
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple13
11Operationoperator: 30
operands: 14
12Operationoperator: 20
operands: 15
13ExprRangelambda_map: 16
start_index: 39
end_index: 29
14ExprTuple17, 33
15ExprTuple18
16Lambdaparameter: 38
body: 19
17Operationoperator: 20
operands: 21
18ExprRangelambda_map: 22
start_index: 39
end_index: 29
19Operationoperator: 23
operands: 24
20Literal
21ExprTuple25
22Lambdaparameter: 38
body: 26
23Literal
24ExprTuple32, 27
25ExprRangelambda_map: 28
start_index: 39
end_index: 29
26Operationoperator: 30
operands: 31
27Literal
28Lambdaparameter: 38
body: 32
29Variable
30Literal
31ExprTuple32, 33
32IndexedVarvariable: 34
index: 38
33Operationoperator: 36
operands: 37
34Variable
35ExprTuple38
36Literal
37ExprTuple39, 40
38Variable
39Literal
40Literal