Expression of type And

from the theory of proveit.numbers.addition.subtraction

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, Variable, a, b, c, d, e, i, j, k
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), InSet(b, Complex), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), Complex), one, j), InSet(d, Complex), ExprRange(sub_expr1, InSet(IndexedVar(e, sub_expr1), Complex), one, k), Equals(b, d))

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