Expression of type ExprTuple

from the theory of proveit.logic.sets.functions.injections

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, C, Conditional, ExprTuple, Lambda, f
from proveit.logic import Forall, InSet, Injections, SubsetEq

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A, B, C], Conditional(Forall(instance_param_or_params = [f], instance_expr = InSet(f, Injections(A, C)), domain = Injections(B, C)), 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, C\right) \mapsto \left\{\forall_{f \in \left[B \xrightarrow[]{\text{1-to-1}} C\right]}~\left(f \in \left[A \xrightarrow[]{\text{1-to-1}} C\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	24, 25, 26
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	24, 25
10	Lambda	parameter: 19 body: 12
11	ExprTuple	19
12	Conditional	value: 13 condition: 14
13	Operation	operator: 16 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	19, 18
16	Literal
17	ExprTuple	19, 20
18	Operation	operator: 22 operands: 21
19	Variable
20	Operation	operator: 22 operands: 23
21	ExprTuple	24, 26
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Variable
26	Variable