Expression of type Conditional

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, B, Conditional, S, f
from proveit.logic import Forall, Functions, Image, SubsetEq

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [f], instance_expr = SubsetEq(Image(f, S), B), domain = Functions(A, B)), SubsetEq(S, 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\{\forall_{f \in \left[A \rightarrow B\right]}~\left(f^{\rightarrow}(S) \subseteq B\right) \textrm{ if } S \subseteq A\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 11 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	22, 23
6	Lambda	parameter: 21 body: 8
7	ExprTuple	21
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 24
13	Literal
14	ExprTuple	21, 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24
21	Variable
22	Variable
23	Variable
24	Variable