Expression of type Lambda

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

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, S, f
from proveit.logic import Forall, Functions, Image, SubsetEq

# build up the expression from sub-expressions
expr = Lambda([A, B, S], Conditional(Forall(instance_param_or_params = [f], instance_expr = SubsetEq(Image(f, S), B), domain = Functions(A, B)), SubsetEq(S, A)))

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, S\right) \mapsto \left\{\forall_{f \in \left[A \rightarrow B\right]}~\left(f^{\rightarrow}(S) \subseteq B\right) \textrm{ if } S \subseteq A\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	25, 26, 24
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 13 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	24, 25
8	Lambda	parameter: 23 body: 10
9	ExprTuple	23
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 26
15	Literal
16	ExprTuple	23, 18
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26
23	Variable
24	Variable
25	Variable
26	Variable