Proof: Write End Decrement If Tab 14

Let's prove the following theorem:

if the following are true:

the line at time 14 = 5
the tab at time 14 = 1
number of lines = 5 - 1
Control Map at time 14 = [ entry 0: (pair ("if", False)), [ ] ]

then the tab at time 15 = 0

Proof:

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Given

1	the line at time 14 = 5
2	the tab at time 14 = 1
3	number of lines = 5 - 1
4	Control Map at time 14 = [ entry 0: (pair ("if", False)), [ ] ]

Proof Table

#	Claim	Reason
1	value at (1 - 1) in map (Control Map at time 14) = pair ("if", False)	if Control Map at time 14 = [ entry 0: (pair ("if", False)), [ ] ], then value at (1 - 1) in map (Control Map at time 14) = pair ("if", False) (Get Decrement Key Value Control Map At 14)
2	the tab at time (14 + 1) = 1 - 1	if the line at time 14 = 5 and the tab at time 14 = 1 and number of lines = 5 - 1 and value at (1 - 1) in map (Control Map at time 14) = pair ("if", False), then the tab at time (14 + 1) = 1 - 1 (Decrement Tab At If End (2))
3	1 - 1 = 0	1 - 1 = 0 (Fixed Value Statement)
4	the tab at time (14 + 1) = 0	if the tab at time (14 + 1) = 1 - 1 and 1 - 1 = 0, then the tab at time (14 + 1) = 0 (Transitive Property of Equality)
5	14 + 1 = 15	14 + 1 = 15 (Fixed Value Statement)
6	the tab at time (14 + 1) = the tab at time 15	if 14 + 1 = 15, then the tab at time (14 + 1) = the tab at time 15 (Substitution)
7	the tab at time 15 = 0	if the tab at time (14 + 1) = the tab at time 15 and the tab at time (14 + 1) = 0, then the tab at time 15 = 0 (Transitive Property of Equality Variation 2)

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