Proof: Write Assign Const Vars 25

Let's prove the following theorem:

if the following are true:

the line at time 25 = 6
the tab at time 25 = 1
statement at line 6, tab 1 = a = 9
9 is constant
Variables Map at time 25 = [ ]

then Variables Map at time 26 = [ entry a: 9, [ ] ]

Proof:

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Given

1	the line at time 25 = 6
2	the tab at time 25 = 1
3	statement at line 6, tab 1 = `a = 9`
4	9 is constant
5	Variables Map at time 25 = [ ]

Proof Table

#	Claim	Reason
1	Variables Map at time (25 + 1) = result of storing 9 at key: a in map: (Variables Map at time 25)	if the line at time 25 = 6 and the tab at time 25 = 1 and statement at line 6, tab 1 = `a = 9` and 9 is constant, then Variables Map at time (25 + 1) = result of storing 9 at key: a in map: (Variables Map at time 25) (Constant Assignment Property)
2	result of storing 9 at key: a in map: (Variables Map at time 25) = result of storing 9 at key: a in map: [ ]	if Variables Map at time 25 = [ ], then result of storing 9 at key: a in map: (Variables Map at time 25) = result of storing 9 at key: a in map: [ ] (Substitution)
3	result of storing 9 at key: a in map: [ ] = [ entry a: 9, [ ] ]	result of storing 9 at key: a in map: [ ] = [ entry a: 9, [ ] ] (do_set_key_value_25_0)
4	result of storing 9 at key: a in map: (Variables Map at time 25) = [ entry a: 9, [ ] ]	if result of storing 9 at key: a in map: (Variables Map at time 25) = result of storing 9 at key: a in map: [ ] and result of storing 9 at key: a in map: [ ] = [ entry a: 9, [ ] ], then result of storing 9 at key: a in map: (Variables Map at time 25) = [ entry a: 9, [ ] ] (Transitive Property of Equality)
5	Variables Map at time (25 + 1) = [ entry a: 9, [ ] ]	if Variables Map at time (25 + 1) = result of storing 9 at key: a in map: (Variables Map at time 25) and result of storing 9 at key: a in map: (Variables Map at time 25) = [ entry a: 9, [ ] ], then Variables Map at time (25 + 1) = [ entry a: 9, [ ] ] (Transitive Property of Equality)
6	25 + 1 = 26	25 + 1 = 26 (Fixed Value Statement)
7	Variables Map at time (25 + 1) = Variables Map at time 26	if 25 + 1 = 26, then Variables Map at time (25 + 1) = Variables Map at time 26 (Substitution)
8	Variables Map at time 26 = [ entry a: 9, [ ] ]	if Variables Map at time (25 + 1) = Variables Map at time 26 and Variables Map at time (25 + 1) = [ entry a: 9, [ ] ], then Variables Map at time 26 = [ entry a: 9, [ ] ] (Transitive Property of Equality Variation 2)

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