Common each_Nk_is_partial_sum of type And

from the theory of proveit.physics.quantum.circuits

import proveit
# Automation is not needed when only 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 the special expression
from proveit.physics.quantum.circuits import each_Nk_is_partial_sum

# check that the built expression is the same as the stored expression
assert each_Nk_is_partial_sum == stored_expr
assert each_Nk_is_partial_sum._style_id == stored_expr._style_id
print("Passed sanity check: each_Nk_is_partial_sum matches stored_expr")

Passed sanity check: each_Nk_is_partial_sum matches stored_expr

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

\left(N_{0} = 0\right)\land \left(N_{1} = \left(N_{1 - 1} + n_{1}\right)\right) \land  \left(N_{2} = \left(N_{2 - 1} + n_{2}\right)\right) \land  \ldots \land  \left(N_{m} = \left(N_{m - 1} + n_{m}\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
3	Operation	operator: 11 operands: 5
4	ExprRange	lambda_map: 6 start_index: 30 end_index: 7
5	ExprTuple	8, 13
6	Lambda	parameter: 26 body: 9
7	Variable
8	IndexedVar	variable: 19 index: 13
9	Operation	operator: 11 operands: 12
10	ExprTuple	13
11	Literal
12	ExprTuple	14, 15
13	Literal
14	IndexedVar	variable: 19 index: 26
15	Operation	operator: 24 operands: 16
16	ExprTuple	17, 18
17	IndexedVar	variable: 19 index: 23
18	IndexedVar	variable: 21 index: 26
19	Variable
20	ExprTuple	23
21	Variable
22	ExprTuple	26
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Operation	operator: 28 operand: 30
28	Literal
29	ExprTuple	30
30	Literal