Expression of type And

from the theory of proveit.numbers.division

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, m, n, w, x, y, z
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import Complex, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(w, sub_expr1)
sub_expr3 = IndexedVar(z, sub_expr1)
expr = And(ExprRange(sub_expr1, InSet(sub_expr2, Complex), one, m), InSet(x, Complex), InSet(y, Complex), ExprRange(sub_expr1, InSet(sub_expr3, Complex), one, n), NotEquals(y, zero), ExprRange(sub_expr1, NotEquals(sub_expr2, zero), one, m), ExprRange(sub_expr1, NotEquals(sub_expr3, zero), one, n))

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(w_{1} \in \mathbb{C}\right) \land  \left(w_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(w_{m} \in \mathbb{C}\right) \land \left(x \in \mathbb{C}\right) \land \left(y \in \mathbb{C}\right)\land \left(z_{1} \in \mathbb{C}\right) \land  \left(z_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(z_{n} \in \mathbb{C}\right) \land \left(y \neq 0\right)\land \left(w_{1} \neq 0\right) \land  \left(w_{2} \neq 0\right) \land  \ldots \land  \left(w_{m} \neq 0\right)\land \left(z_{1} \neq 0\right) \land  \left(z_{2} \neq 0\right) \land  \ldots \land  \left(z_{n} \neq 0\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, 9
3	ExprRange	lambda_map: 10 start_index: 18 end_index: 16
4	Operation	operator: 27 operands: 11
5	Operation	operator: 27 operands: 12
6	ExprRange	lambda_map: 13 start_index: 18 end_index: 19
7	Operation	operator: 30 operands: 14
8	ExprRange	lambda_map: 15 start_index: 18 end_index: 16
9	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
10	Lambda	parameter: 39 body: 20
11	ExprTuple	21, 32
12	ExprTuple	23, 32
13	Lambda	parameter: 39 body: 22
14	ExprTuple	23, 35
15	Lambda	parameter: 39 body: 24
16	Variable
17	Lambda	parameter: 39 body: 25
18	Literal
19	Variable
20	Operation	operator: 27 operands: 26
21	Variable
22	Operation	operator: 27 operands: 28
23	Variable
24	Operation	operator: 30 operands: 29
25	Operation	operator: 30 operands: 31
26	ExprTuple	33, 32
27	Literal
28	ExprTuple	34, 32
29	ExprTuple	33, 35
30	Literal
31	ExprTuple	34, 35
32	Literal
33	IndexedVar	variable: 36 index: 39
34	IndexedVar	variable: 37 index: 39
35	Literal
36	Variable
37	Variable
38	ExprTuple	39
39	Variable