Expression of type Equals

from the theory of proveit.numbers.ordering

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, b, d
from proveit.logic import Equals, FALSE
from proveit.numbers import Less, LessEq

# build up the expression from sub-expressions
expr = Equals(ConditionalSet(Conditional(d, LessEq(d, b)), Conditional(b, Less(b, d))), ConditionalSet(d, Conditional(b, FALSE))).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left\{\begin{array}{ccc}d \textrm{ if } d \leq b \\ b \textrm{ if } b < d\end{array}\right.. =  \\ \left\{\begin{array}{ccc}d \\ b \textrm{ if } \bot\end{array}\right.. \end{array} \end{array}

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.	()	(2)	('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, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	19, 10
8	Conditional	value: 19 condition: 11
9	Conditional	value: 18 condition: 12
10	Conditional	value: 18 condition: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Literal
14	Literal
15	ExprTuple	19, 18
16	Literal
17	ExprTuple	18, 19
18	Variable
19	Variable