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Expression of type Forall

from the theory of proveit.numbers.absolute_value

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 theta
from proveit.logic import Equals, Forall
from proveit.numbers import Abs, Exp, Mult, Real, e, i, one
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [theta], instance_expr = Equals(Abs(Exp(e, Mult(i, theta))), one), domain = Real)
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_{\theta \in \mathbb{R}}~\left(\left|\mathsf{e}^{\mathsf{i} \cdot \theta}\right| = 1\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
3Lambdaparameter: 25
body: 5
4ExprTuple25
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12, 13
10Literal
11ExprTuple25, 14
12Operationoperator: 15
operand: 17
13Literal
14Literal
15Literal
16ExprTuple17
17Operationoperator: 18
operands: 19
18Literal
19ExprTuple20, 21
20Literal
21Operationoperator: 22
operands: 23
22Literal
23ExprTuple24, 25
24Literal
25Variable