Expression of type Lambda

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

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	23, 24, 25
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	23, 24
9	Lambda	parameter: 18 body: 11
10	ExprTuple	18
11	Conditional	value: 12 condition: 13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	18, 17
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 21 operands: 20
18	Variable
19	Operation	operator: 21 operands: 22
20	ExprTuple	23, 25
21	Literal
22	ExprTuple	24, 25
23	Variable
24	Variable
25	Variable