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, Conditional, 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(f, Conditional(And(InSet(f, Functions(A, B)), Forall(instance_param_or_params = [a, b], instance_expr = NotEquals(fa, fb), domain = A, condition = NotEquals(a, b))), InSet(f, 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())

f \mapsto \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] \textrm{ if } f \in \left[A \xrightarrow[]{\text{1-to-1}} B\right]\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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