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, Q, f, g, i
from proveit.core_expr_types import Q__a_1_to_i, Q__b_1_to_i, Q__c_1_to_i, 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, Q], 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), condition = Q__a_1_to_i), Equals(Lambda([b_1_to_i], Conditional(f__b_1_to_i, Q__b_1_to_i)), Lambda([c_1_to_i], Conditional(g__c_1_to_i, Q__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, Q}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{a_{1}, a_{2}, \ldots, a_{i}~|~Q\left(a_{1}, a_{2}, \ldots, a_{i}\right)}~\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 \left\{f\left(b_{1}, b_{2}, \ldots, b_{i}\right) \textrm{ if } Q\left(b_{1}, b_{2}, \ldots, b_{i}\right)\right..\right] =  \\ \left[\left(c_{1}, c_{2}, \ldots, c_{i}\right) \mapsto \left\{g\left(c_{1}, c_{2}, \ldots, c_{i}\right) \textrm{ if } Q\left(c_{1}, c_{2}, \ldots, c_{i}\right)\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: 50 body: 2
1	ExprTuple	50
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	50, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	40, 41, 34
11	Operation	operator: 12 operands: 13
12	Literal
13	ExprTuple	14, 15
14	Operation	operator: 16 operand: 19
15	Operation	operator: 31 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	20, 21
19	Lambda	parameters: 42 body: 22
20	Lambda	parameters: 33 body: 23
21	Lambda	parameters: 35 body: 24
22	Conditional	value: 25 condition: 26
23	Conditional	value: 27 condition: 28
24	Conditional	value: 29 condition: 30
25	Operation	operator: 31 operands: 32
26	Operation	operator: 34 operands: 42
27	Operation	operator: 40 operands: 33
28	Operation	operator: 34 operands: 33
29	Operation	operator: 41 operands: 35
30	Operation	operator: 34 operands: 35
31	Literal
32	ExprTuple	36, 37
33	ExprTuple	38
34	Variable
35	ExprTuple	39
36	Operation	operator: 40 operands: 42
37	Operation	operator: 41 operands: 42
38	ExprRange	lambda_map: 43 start_index: 49 end_index: 50
39	ExprRange	lambda_map: 44 start_index: 49 end_index: 50
40	Variable
41	Variable
42	ExprTuple	45
43	Lambda	parameter: 56 body: 46
44	Lambda	parameter: 56 body: 47
45	ExprRange	lambda_map: 48 start_index: 49 end_index: 50
46	IndexedVar	variable: 51 index: 56
47	IndexedVar	variable: 52 index: 56
48	Lambda	parameter: 56 body: 53
49	Literal
50	Variable
51	Variable
52	Variable
53	IndexedVar	variable: 54 index: 56
54	Variable
55	ExprTuple	56
56	Variable