Expression of type Implies

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 Lambda
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

# build up the expression from sub-expressions
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)

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())

\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}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

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