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Proof step 2 from proof log-cons-2 (previous step)

log-cons(log, fs) ⊦ adr0 = adr1, log-cons(log, fs[adr0, nd0][adr1, nd1]), adr1 ∈ fs, adr0 ∈ fs

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ log-cons(log, fs) ∧ adr ∈ log → node-cons(fs[adr].key, fs[adr]); (ss)% ⊦ adr ∈ fs ∧ ¬ adr0 ∈ fs → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)%⊦ log-cons(log, fs) → ( log-cons(log0, fs0) ↔ (∀ adr. (adr ∈ log → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr])) → adr ∈ log0 → adr ∈ fs0 ∧ node-cons(fs0[adr].key, fs0[adr]))); (ss)