Expression of type Equals

from the theory of proveit.core_expr_types.conditionals

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 Conditional, ConditionalSet, ExprRange, IndexedVar, Variable, a, b, c, m, n
from proveit.logic import Equals, FALSE
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(ConditionalSet(ExprRange(sub_expr1, Conditional(IndexedVar(a, sub_expr1), FALSE), one, m), b, ExprRange(sub_expr1, Conditional(IndexedVar(c, sub_expr1), FALSE), one, n)), b)

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\{\begin{array}{ccc}a_{1} \textrm{ if } \bot \\ a_{2} \textrm{ if } \bot \\  \vdots \\ a_{m} \textrm{ if } \bot \\ b \\ c_{1} \textrm{ if } \bot \\ c_{2} \textrm{ if } \bot \\  \vdots \\ c_{n} \textrm{ if } \bot\end{array}\right.. = b

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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 7
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7, 8
6	ExprRange	lambda_map: 9 start_index: 12 end_index: 10
7	Variable
8	ExprRange	lambda_map: 11 start_index: 12 end_index: 13
9	Lambda	parameter: 22 body: 14
10	Variable
11	Lambda	parameter: 22 body: 15
12	Literal
13	Variable
14	Conditional	value: 16 condition: 18
15	Conditional	value: 17 condition: 18
16	IndexedVar	variable: 19 index: 22
17	IndexedVar	variable: 20 index: 22
18	Literal
19	Variable
20	Variable
21	ExprTuple	22
22	Variable