Expression of type And

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, B, a, b, f, fa, fb
from proveit.logic import And, Forall, Functions, InSet, NotEquals

# build up the expression from sub-expressions
expr = And(InSet(f, Functions(A, B)), Forall(instance_param_or_params = [a, b], instance_expr = NotEquals(fa, fb), domain = A, condition = 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 \in \left[A \rightarrow B\right]\right) \land \left[\forall_{a, b \in A~|~a \neq b}~\left(f\left(a\right) \neq f\left(b\right)\right)\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: 16 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 27 operands: 4
3	Operation	operator: 5 operand: 8
4	ExprTuple	24, 7
5	Literal
6	ExprTuple	8
7	Operation	operator: 9 operands: 10
8	Lambda	parameters: 30 body: 11
9	Literal
10	ExprTuple	31, 12
11	Conditional	value: 13 condition: 14
12	Variable
13	Operation	operator: 29 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22
18	Operation	operator: 24 operand: 32
19	Operation	operator: 24 operand: 33
20	Operation	operator: 27 operands: 26
21	Operation	operator: 27 operands: 28
22	Operation	operator: 29 operands: 30
23	ExprTuple	32
24	Variable
25	ExprTuple	33
26	ExprTuple	32, 31
27	Literal
28	ExprTuple	33, 31
29	Literal
30	ExprTuple	32, 33
31	Variable
32	Variable
33	Variable