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 e, m
from proveit.logic import Forall, TRUE
from proveit.numbers import ModAbs, greater, subtract
from proveit.physics.quantum.QPE import _b_floor, _m_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m], instance_expr = TRUE, domain = _m_domain, condition = greater(ModAbs(subtract(m, _b_floor), _two_pow_t), e))

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_{m \in \{0~\ldotp \ldotp~2^{t} - 1\}~|~\left|m - b_{\textit{f}}\right|_{\textup{mod}\thinspace 2^{t}} > e}~\top

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: 31 body: 5
4	ExprTuple	31
5	Conditional	value: 6 condition: 7
6	Literal
7	Operation	operator: 8 operands: 9
8	Literal
9	ExprTuple	10, 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	31, 16
14	Literal
15	ExprTuple	17, 18
16	Operation	operator: 19 operands: 20
17	Variable
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 29
23	Literal
24	Operation	operator: 27 operands: 26
25	Operation	operator: 27 operands: 28
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31, 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 36 operand: 40
31	Variable
32	Operation	operator: 36 operand: 41
33	Literal
34	ExprTuple	38, 39
35	ExprTuple	40
36	Literal
37	ExprTuple	41
38	Literal
39	Literal
40	Literal
41	Literal