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Proof step 7 from proof RED-complete (previous step)

〈RED1(t'; tn)〉 tn = tn1, ∀ n0, t', t. n0 < 0 → (irred(t') ∧ (=> ^ n0)(t, t') → 〈RED(t; t0)〉 t0 = t'), irred(t'), tn1 = none ⊃ irred(t') ; t' => tn1 .t ⊦ 〈if tn1 ≠ none then RED(tn1 .t; t1) else t1 := t'〉 t1 = t'

Heuristic conditional right split applied rule if right

And obtained the following new goals

Proof step 5:
〈RED1(t'; tn)〉 tn = tn1, ∀ n0, t', t. n0 < 0 → (irred(t') ∧ (=> ^ n0)(t, t') → 〈RED(t; t0)〉 t0 = t'), irred(t'), tn1 = none ⊃ irred(t') ; t' => tn1 .t, tn1 ≠ none ⊦ 〈RED(tn1 .t; t1)〉 t1 = t'
Proof step 6:
〈RED1(t'; tn)〉 tn = tn1, ∀ n0, t', t. n0 < 0 → (irred(t') ∧ (=> ^ n0)(t, t') → 〈RED(t; t0)〉 t0 = t'), irred(t'), tn1 = none ⊃ irred(t') ; t' => tn1 .t, ¬ tn1 ≠ none ⊦ 〈t1 := t'〉 t1 = t'

Rule argument

[fmapos-arg: pos: right 1]

Additional information

[[CONCRETESIMPRULES : ()]]