Expression of type Lambda

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

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, f, fx, x
from proveit.logic import Bijections, Forall, InSet

# build up the expression from sub-expressions
sub_expr1 = Bijections(A, B)
expr = Lambda([A, B], Forall(instance_param_or_params = [f], instance_expr = InSet(f, sub_expr1), condition = InSet(Lambda(x, Conditional(fx, InSet(x, A))), sub_expr1)))

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~|~\left[x \mapsto \left\{f\left(x\right) \textrm{ if } x \in A\right..\right] \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right]}~\left(f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\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: 15 body: 1
1	Operation	operator: 2 operand: 4
2	Literal
3	ExprTuple	4
4	Lambda	parameter: 19 body: 6
5	ExprTuple	19
6	Conditional	value: 7 condition: 8
7	Operation	operator: 21 operands: 9
8	Operation	operator: 21 operands: 10
9	ExprTuple	19, 12
10	ExprTuple	11, 12
11	Lambda	parameter: 23 body: 13
12	Operation	operator: 14 operands: 15
13	Conditional	value: 16 condition: 17
14	Literal
15	ExprTuple	24, 18
16	Operation	operator: 19 operand: 23
17	Operation	operator: 21 operands: 22
18	Variable
19	Variable
20	ExprTuple	23
21	Literal
22	ExprTuple	23, 24
23	Variable
24	Variable