Expression of type ExprTuple

from the theory of proveit.logic.sets

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, x
from proveit.logic import Boolean, Forall, InSet, Intersect, SubsetEq

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A, B], Conditional(SubsetEq(Intersect(A, B), A), Forall(instance_param_or_params = [x], instance_expr = InSet(InSet(x, B), Boolean)))))

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\right) \mapsto \left\{\left(A \cap B\right) \subseteq A \textrm{ if } \forall_{x}~\left(\left(x \in B\right) \in \mathbb{B}\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: 12 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operand: 10
5	Literal
6	ExprTuple	9, 15
7	Literal
8	ExprTuple	10
9	Operation	operator: 11 operands: 12
10	Lambda	parameter: 21 body: 14
11	Literal
12	ExprTuple	15, 22
13	ExprTuple	21
14	Operation	operator: 19 operands: 16
15	Variable
16	ExprTuple	17, 18
17	Operation	operator: 19 operands: 20
18	Literal
19	Literal
20	ExprTuple	21, 22
21	Variable
22	Variable