Expression of type ExprTuple

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, ExprTuple, Lambda, S, f
from proveit.logic import Forall, Functions, Image, SubsetEq

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A, B, S], 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(\left(A, B, S\right) \mapsto \left\{\forall_{f \in \left[A \rightarrow B\right]}~\left(f^{\rightarrow}(S) \subseteq B\right) \textrm{ if } S \subseteq A\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	26, 27, 25
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 14 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	25, 26
9	Lambda	parameter: 24 body: 11
10	ExprTuple	24
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 27
16	Literal
17	ExprTuple	24, 19
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27
24	Variable
25	Variable
26	Variable
27	Variable