Expression of type And

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, Variable, t
from proveit.logic import And, Equals
from proveit.numbers import Add, Neg, one, two, zero
from proveit.physics.quantum.QPE import _s

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, _s)
expr = And(Equals(zero, zero), Equals(one, Add(zero, one)), And(ExprRange(sub_expr1, Equals(Add(sub_expr1, t), Add(Add(sub_expr1, Neg(one), t), one)), Add(Neg(t), two), zero)), Equals(sub_expr2, sub_expr2))

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(0 = 0\right) \land \left(1 = \left(0 + 1\right)\right) \land \left(\left(\left(\left(-t + 2\right) + t\right) = \left(\left(\left(-t + 2\right) - 1 + t\right) + 1\right)\right) \land  \left(\left(\left(-t + 3\right) + t\right) = \left(\left(\left(-t + 3\right) - 1 + t\right) + 1\right)\right) \land  \ldots \land  \left(\left(0 + t\right) = \left(\left(0 - 1 + t\right) + 1\right)\right)\right) \land \left(\left(t + s\right) = \left(t + s\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 8 operands: 1
1	ExprTuple	2, 3, 4, 5
2	Operation	operator: 23 operands: 6
3	Operation	operator: 23 operands: 7
4	Operation	operator: 8 operands: 9
5	Operation	operator: 23 operands: 10
6	ExprTuple	18, 18
7	ExprTuple	40, 11
8	Literal
9	ExprTuple	12
10	ExprTuple	13, 13
11	Operation	operator: 33 operands: 14
12	ExprRange	lambda_map: 15 start_index: 16 end_index: 18
13	Operation	operator: 33 operands: 17
14	ExprTuple	18, 40
15	Lambda	parameter: 35 body: 20
16	Operation	operator: 33 operands: 21
17	ExprTuple	37, 22
18	Literal
19	ExprTuple	35
20	Operation	operator: 23 operands: 24
21	ExprTuple	25, 26
22	Literal
23	Literal
24	ExprTuple	27, 28
25	Operation	operator: 38 operand: 37
26	Literal
27	Operation	operator: 33 operands: 30
28	Operation	operator: 33 operands: 31
29	ExprTuple	37
30	ExprTuple	35, 37
31	ExprTuple	32, 40
32	Operation	operator: 33 operands: 34
33	Literal
34	ExprTuple	35, 36, 37
35	Variable
36	Operation	operator: 38 operand: 40
37	Variable
38	Literal
39	ExprTuple	40
40	Literal