Expression of type Forall

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 = 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))

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())

\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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 9 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	33, 34, 27
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 24 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	13, 14
12	Lambda	parameters: 35 body: 15
13	Lambda	parameters: 26 body: 16
14	Lambda	parameters: 28 body: 17
15	Conditional	value: 18 condition: 19
16	Conditional	value: 20 condition: 21
17	Conditional	value: 22 condition: 23
18	Operation	operator: 24 operands: 25
19	Operation	operator: 27 operands: 35
20	Operation	operator: 33 operands: 26
21	Operation	operator: 27 operands: 26
22	Operation	operator: 34 operands: 28
23	Operation	operator: 27 operands: 28
24	Literal
25	ExprTuple	29, 30
26	ExprTuple	31
27	Variable
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