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Proof step 9 from proof RED-complete (previous step)

∀ n0, t', t. n0 < 0 → (irred(t') ∧ (=> ^ n0)(t, t') → 〈RED(t; t0)〉 t0 = t'), irred(t') ⊦ 〈RED1(t'; tn0)〉〈if tn0 ≠ none then RED(tn0 .t; t1) else t1 := t'〉 t1 = t'

User applied rule insert lemma

And obtained the following new goals

Proof step 4:
⊦ 〈RED1(t; tn)〉 (tn = none ⊃ irred(t); t => tn .t)
Proof step 8:
〈RED1(t'; tn)〉 (tn = none ⊃ irred(t'); t' => tn .t), ∀ n0, t', t. n0 < 0 → (irred(t') ∧ (=> ^ n0)(t, t') → 〈RED(t; t0)〉 t0 = t'), irred(t') ⊦ 〈RED1(t'; tn0)〉〈if tn0 ≠ none then RED(tn0 .t; t1) else t1 := t'〉 t1 = t'

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: RED1-lem antecedent: succedent: 〈RED1(t; tn)〉 (tn = none ⊃ ¬ (∃ t0. t => t0); t => tn .t) substlist: [t] → [t'] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (t')]]