Expression of type Forall

from the theory of proveit.physics.quantum.QPE

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 l
from proveit.logic import Equals, Forall
from proveit.numbers import Abs, ModAbs
from proveit.physics.quantum.QPE import _full_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l], instance_expr = Equals(ModAbs(l, _two_pow_t), Abs(l)), domain = _full_domain)

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}}~\left(\left|l\right|_{\textup{mod}\thinspace 2^{t}} = \left|l\right|\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 21 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	21, 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operand: 21
13	Operation	operator: 18 operands: 19
14	Literal
15	ExprTuple	21, 20
16	Literal
17	ExprTuple	21
18	Literal
19	ExprTuple	22, 27
20	Operation	operator: 28 operands: 23
21	Variable
22	Operation	operator: 32 operands: 24
23	ExprTuple	30, 34
24	ExprTuple	25, 38
25	Operation	operator: 36 operand: 27
26	ExprTuple	27
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Literal
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	34, 35
34	Literal
35	Operation	operator: 36 operand: 38
36	Literal
37	ExprTuple	38
38	Literal