Axiom lambda_substitution of type Forall

from the theory of proveit.core_expr_types.lambda_maps

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_axiom_expr # Load the stored axiom expression as 'stored_expr'
# import the special expression
from proveit.core_expr_types.lambda_maps import lambda_substitution

# check that the built expression is the same as the stored expression
assert lambda_substitution.expr == stored_expr
assert lambda_substitution.expr._style_id == stored_expr._style_id
print("Passed sanity check: lambda_substitution matches stored_expr")

Passed sanity check: lambda_substitution matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{i \in \mathbb{N}^+}~\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)\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: 18 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 45 body: 4
3	ExprTuple	45
4	Conditional	value: 5 condition: 6
5	Operation	operator: 18 operand: 10
6	Operation	operator: 8 operands: 9
7	ExprTuple	10
8	Literal
9	ExprTuple	45, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	35, 36
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 18 operand: 21
17	Operation	operator: 27 operands: 20
18	Literal
19	ExprTuple	21
20	ExprTuple	22, 23
21	Lambda	parameters: 37 body: 24
22	Lambda	parameters: 29 body: 25
23	Lambda	parameters: 30 body: 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 35 operands: 29
26	Operation	operator: 36 operands: 30
27	Literal
28	ExprTuple	31, 32
29	ExprTuple	33
30	ExprTuple	34
31	Operation	operator: 35 operands: 37
32	Operation	operator: 36 operands: 37
33	ExprRange	lambda_map: 38 start_index: 44 end_index: 45
34	ExprRange	lambda_map: 39 start_index: 44 end_index: 45
35	Variable
36	Variable
37	ExprTuple	40
38	Lambda	parameter: 51 body: 41
39	Lambda	parameter: 51 body: 42
40	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
41	IndexedVar	variable: 46 index: 51
42	IndexedVar	variable: 47 index: 51
43	Lambda	parameter: 51 body: 48
44	Literal
45	Variable
46	Variable
47	Variable
48	IndexedVar	variable: 49 index: 51
49	Variable
50	ExprTuple	51
51	Variable