Expression of type ExprTuple

from the theory of proveit.logic.sets.inclusion

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, P, Px, Py, x, y
from proveit.logic import Exists, Implies, SubsetEq

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A, B, P], Conditional(Implies(Exists(instance_param_or_params = [x], instance_expr = Px, domain = A), Exists(instance_param_or_params = [y], instance_expr = Py, domain = B)), SubsetEq(A, B))))

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, P\right) \mapsto \left\{\left[\exists_{x \in A}~P\left(x\right)\right] \Rightarrow \left[\exists_{y \in B}~P\left(y\right)\right] \textrm{ if } A \subseteq B\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	30, 32, 25
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	30, 32
10	Operation	operator: 13 operand: 15
11	Operation	operator: 13 operand: 16
12	ExprTuple	15
13	Literal
14	ExprTuple	16
15	Lambda	parameter: 29 body: 17
16	Lambda	parameter: 31 body: 18
17	Conditional	value: 19 condition: 20
18	Conditional	value: 21 condition: 22
19	Operation	operator: 25 operand: 29
20	Operation	operator: 27 operands: 24
21	Operation	operator: 25 operand: 31
22	Operation	operator: 27 operands: 28
23	ExprTuple	29
24	ExprTuple	29, 30
25	Variable
26	ExprTuple	31
27	Literal
28	ExprTuple	31, 32
29	Variable
30	Variable
31	Variable
32	Variable