Expression of type Lambda

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

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, Lambda, f, fx, x
from proveit.logic import Equals, Image, SetOfAll

# build up the expression from sub-expressions
expr = Lambda([f, A], Equals(Image(f, A), SetOfAll(instance_param_or_params = [x], instance_element = fx, domain = A)))

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, A\right) \mapsto \left(f^{\rightarrow}(A) = \left\{f\left(x\right)\right\}_{x \in A}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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