Expression of type ExprTuple

from the theory of proveit.logic.sets.functions

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, ExprTuple, Lambda, f, fx, x
from proveit.logic import Equals, Forall, Functions, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, A, B], Equals(InSet(f, Functions(A, B)), Forall(instance_param_or_params = [x], instance_expr = InSet(fx, B), 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(\left(f, A, B\right) \mapsto \left(\left(f \in \left[A \rightarrow B\right]\right) = \left[\forall_{x \in A}~\left(f\left(x\right) \in B\right)\right]\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	24, 23, 22
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 19 operands: 8
7	Operation	operator: 9 operand: 12
8	ExprTuple	24, 11
9	Literal
10	ExprTuple	12
11	Operation	operator: 13 operands: 14
12	Lambda	parameter: 26 body: 15
13	Literal
14	ExprTuple	23, 22
15	Conditional	value: 16 condition: 17
16	Operation	operator: 19 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	26, 23
21	Operation	operator: 24 operand: 26
22	Variable
23	Variable
24	Variable
25	ExprTuple	26
26	Variable