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