Proof: Do Expr At Unchanged 3

Let's prove the following theorem:

if the following are true:
  • expression state at time 3 = "begin_expr"
  • the expression at time 3 = entry "ES": "Estonia"

then the expression at time 4 = entry "ES": "Estonia"

Proof:

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Given
1 expression state at time 3 = "begin_expr"
2 the expression at time 3 = entry "ES": "Estonia"
Proof Table
# Claim Reason
1 the expression at time (3 + 1) = the expression at time 3 if expression state at time 3 = "begin_expr", then the expression at time (3 + 1) = the expression at time 3
2 the expression at time (3 + 1) = entry "ES": "Estonia" if the expression at time (3 + 1) = the expression at time 3 and the expression at time 3 = entry "ES": "Estonia", then the expression at time (3 + 1) = entry "ES": "Estonia"
3 3 + 1 = 4 3 + 1 = 4
4 the expression at time (3 + 1) = the expression at time 4 if 3 + 1 = 4, then the expression at time (3 + 1) = the expression at time 4
5 the expression at time 4 = entry "ES": "Estonia" if the expression at time (3 + 1) = the expression at time 4 and the expression at time (3 + 1) = entry "ES": "Estonia", then the expression at time 4 = entry "ES": "Estonia"

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