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
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

# build up the expression from sub-expressions
expr = Lambda([f, g, Q], 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))

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(f, g, Q\right) \mapsto \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)

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