Expression of type And

from the theory of proveit.physics.quantum.circuits

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, IndexedVar, N, Variable, m
from proveit.logic import And, InSet
from proveit.numbers import Natural, zero
from proveit.physics.quantum.circuits import each_Nk_is_partial_sum

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = And(ExprRange(sub_expr1, InSet(IndexedVar(N, sub_expr1), Natural), zero, m), each_Nk_is_partial_sum)

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(N_{0} \in \mathbb{N}\right) \land  \left(N_{1} \in \mathbb{N}\right) \land  \ldots \land  \left(N_{m} \in \mathbb{N}\right) \land \left(\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)\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: 5 operands: 1
1	ExprTuple	2, 3
2	ExprRange	lambda_map: 4 start_index: 21 end_index: 14
3	Operation	operator: 5 operands: 6
4	Lambda	parameter: 34 body: 7
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 19 operands: 12
9	ExprRange	lambda_map: 13 start_index: 38 end_index: 14
10	Literal
11	ExprTuple	22, 15
12	ExprTuple	16, 21
13	Lambda	parameter: 34 body: 17
14	Variable
15	Literal
16	IndexedVar	variable: 27 index: 21
17	Operation	operator: 19 operands: 20
18	ExprTuple	21
19	Literal
20	ExprTuple	22, 23
21	Literal
22	IndexedVar	variable: 27 index: 34
23	Operation	operator: 32 operands: 24
24	ExprTuple	25, 26
25	IndexedVar	variable: 27 index: 31
26	IndexedVar	variable: 29 index: 34
27	Variable
28	ExprTuple	31
29	Variable
30	ExprTuple	34
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	34, 35
34	Variable
35	Operation	operator: 36 operand: 38
36	Literal
37	ExprTuple	38
38	Literal