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Proof step 16 from proof crash-neutral-unmap (previous step)

# avols[v] = # avols0[v], m0 < # avols0[v], m < # avols0[v], ebm-cons(avols0), ebm-cons(avols), v ∈ avols0, v ∈ avols, ∀ m. m < # avols0[v] ∧ avols[v][m] ≠ unmapped → (avols[v][m] = erased → avols0[v][m] = erased) ∧ (avols[v][m].mapped? → avols0[v][m] = avols[v][m]) ⊦ avols[v][m, unmapped][m0] = unmapped, (avols[v][m0] = erased → avols0[v][m0] = erased) ∧ (avols[v][m0].mapped? → avols0[v][m0] = avols[v][m0])

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 17:
# avols[v] = # avols0[v], m < # avols0[v], m0 < # avols0[v], ebm-cons(avols), ebm-cons(avols0), v ∈ avols, v ∈ avols0, ∀ m. m < # avols0[v] ∧ avols[v][m] ≠ unmapped → (avols[v][m] = erased → avols0[v][m] = erased) ∧ (avols[v][m].mapped? → avols0[v][m] = avols[v][m]) ⊦ avols[v][m, unmapped][m0] = unmapped, m0 = m, (avols[v][m0] = erased → avols0[v][m0] = erased) ∧ (avols[v][m0].mapped? → avols0[v][m0] = avols[v][m0])

Rule argument

fma: m0 = m

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # evol ⊦ evol[m, leb][m] = leb; (s) Used formulas: m0 = m