Expression of type Lambda

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

# build up the expression from sub-expressions
expr = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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