Expression of type Lambda

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

# build up the expression from sub-expressions
expr = Lambda([A, B], Forall(instance_param_or_params = [f], instance_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))), domain = Injections(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(A, B\right) \mapsto \left[\forall_{f \in \left[A \xrightarrow[]{\text{1-to-1}} B\right]}~\left(\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]\right)\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 20 body: 1
1	Operation	operator: 14 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 34 body: 5
4	ExprTuple	34
5	Conditional	value: 6 condition: 7
6	Operation	operator: 26 operands: 8
7	Operation	operator: 37 operands: 9
8	ExprTuple	10, 11
9	ExprTuple	34, 12
10	Operation	operator: 37 operands: 13
11	Operation	operator: 14 operand: 18
12	Operation	operator: 16 operands: 20
13	ExprTuple	34, 17
14	Literal
15	ExprTuple	18
16	Literal
17	Operation	operator: 19 operands: 20
18	Lambda	parameters: 40 body: 21
19	Literal
20	ExprTuple	41, 22
21	Conditional	value: 23 condition: 24
22	Variable
23	Operation	operator: 39 operands: 25
24	Operation	operator: 26 operands: 27
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30, 31, 32
28	Operation	operator: 34 operand: 42
29	Operation	operator: 34 operand: 43
30	Operation	operator: 37 operands: 36
31	Operation	operator: 37 operands: 38
32	Operation	operator: 39 operands: 40
33	ExprTuple	42
34	Variable
35	ExprTuple	43
36	ExprTuple	42, 41
37	Literal
38	ExprTuple	43, 41
39	Literal
40	ExprTuple	42, 43
41	Variable
42	Variable
43	Variable