Expression of type Lambda

from the theory of proveit.core_expr_types.lambda_maps

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 Conditional, Lambda, f, g, i
from proveit.core_expr_types import a_1_to_i, b_1_to_i, c_1_to_i, f__a_1_to_i, f__b_1_to_i, g__a_1_to_i, g__c_1_to_i
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Lambda(i, Conditional(Forall(instance_param_or_params = [f, g], instance_expr = Implies(Forall(instance_param_or_params = [a_1_to_i], instance_expr = Equals(f__a_1_to_i, g__a_1_to_i)), Equals(Lambda([b_1_to_i], f__b_1_to_i), Lambda([c_1_to_i], g__c_1_to_i)).with_wrapping_at(2)).with_wrapping_at(2)), InSet(i, NaturalPos)))

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())

i \mapsto \left\{\forall_{f, g}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{a_{1}, a_{2}, \ldots, a_{i}}~\left(f\left(a_{1}, a_{2}, \ldots, a_{i}\right) = g\left(a_{1}, a_{2}, \ldots, a_{i}\right)\right)\right] \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left[\left(b_{1}, b_{2}, \ldots, b_{i}\right) \mapsto f\left(b_{1}, b_{2}, \ldots, b_{i}\right)\right] =  \\ \left[\left(c_{1}, c_{2}, \ldots, c_{i}\right) \mapsto g\left(c_{1}, c_{2}, \ldots, c_{i}\right)\right] \end{array} \end{array}\right) \end{array} \end{array}\right) \textrm{ if } i \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 43 body: 2
1	ExprTuple	43
2	Conditional	value: 3 condition: 4
3	Operation	operator: 16 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	43, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	33, 34
11	Operation	operator: 12 operands: 13
12	Literal
13	ExprTuple	14, 15
14	Operation	operator: 16 operand: 19
15	Operation	operator: 25 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	20, 21
19	Lambda	parameters: 35 body: 22
20	Lambda	parameters: 27 body: 23
21	Lambda	parameters: 28 body: 24
22	Operation	operator: 25 operands: 26
23	Operation	operator: 33 operands: 27
24	Operation	operator: 34 operands: 28
25	Literal
26	ExprTuple	29, 30
27	ExprTuple	31
28	ExprTuple	32
29	Operation	operator: 33 operands: 35
30	Operation	operator: 34 operands: 35
31	ExprRange	lambda_map: 36 start_index: 42 end_index: 43
32	ExprRange	lambda_map: 37 start_index: 42 end_index: 43
33	Variable
34	Variable
35	ExprTuple	38
36	Lambda	parameter: 49 body: 39
37	Lambda	parameter: 49 body: 40
38	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
39	IndexedVar	variable: 44 index: 49
40	IndexedVar	variable: 45 index: 49
41	Lambda	parameter: 49 body: 46
42	Literal
43	Variable
44	Variable
45	Variable
46	IndexedVar	variable: 47 index: 49
47	Variable
48	ExprTuple	49
49	Variable