Expression of type ExprTuple

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 ExprRange, ExprTuple, Variable, t
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Interval, Neg, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(Add(sub_expr1, Add(Neg(t), one)), Neg(one), t)
expr = ExprTuple(Forall(instance_param_or_params = [sub_expr1], instance_expr = Equals(sub_expr2, sub_expr1), domain = Interval(one, t)), Equals([ExprRange(sub_expr1, sub_expr2, one, t)], [ExprRange(sub_expr1, sub_expr1, one, t)]))

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())

\left(\forall_{{_{-}a} \in \{1~\ldotp \ldotp~t\}}~\left(\left(\left({_{-}a} + \left(-t + 1\right)\right) - 1 + t\right) = {_{-}a}\right), \left(\left(\left(1 + \left(-t + 1\right)\right) - 1 + t\right), \left(\left(2 + \left(-t + 1\right)\right) - 1 + t\right), \ldots, \left(\left(t + \left(-t + 1\right)\right) - 1 + t\right)\right) = \left(1, 2, \ldots, t\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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