Expression of type Conditional

from the theory of proveit.logic.sets.functions.injections

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 A, Conditional, a, b, fa, fb
from proveit.logic import And, InSet, NotEquals

# build up the expression from sub-expressions
expr = Conditional(NotEquals(fa, fb), And(InSet(a, A), InSet(b, A), NotEquals(a, 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\{f\left(a\right) \neq f\left(b\right) \textrm{ if } a \in A ,  b \in A ,  a \neq b\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 17 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10
6	Operation	operator: 12 operand: 20
7	Operation	operator: 12 operand: 21
8	Operation	operator: 15 operands: 14
9	Operation	operator: 15 operands: 16
10	Operation	operator: 17 operands: 18
11	ExprTuple	20
12	Variable
13	ExprTuple	21
14	ExprTuple	20, 19
15	Literal
16	ExprTuple	21, 19
17	Literal
18	ExprTuple	20, 21
19	Variable
20	Variable
21	Variable