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Proof step 19 from proof crash-neutral-unmap (previous step)

v0 ∈ avols ↔ v0 ∈ avols0, m < # avols[v], ebm-cons(avols0), ebm-cons(avols), v ∈ avols, v0 ∈ avols0 → # avols[v0] = # avols0[v0] ∧ (∀ m. m < # avols[v0] ∧ avols[v0][m] ≠ unmapped → (avols[v0][m] = erased → avols0[v0][m] = erased) ∧ (avols[v0][m].mapped? → avols0[v0][m] = avols[v0][m])) ⊦ v0 = v, (v0 ∈ avols[v, avols[v][m, unmapped]] ↔ v0 ∈ avols0) ∧ ( v0 ∈ avols[v, avols[v][m, unmapped]] → # avols[v, avols[v][m, unmapped]][v0] = # avols0[v0] ∧ ( m0 < # avols[v, avols[v][m, unmapped]][v0] ∧ avols[v, avols[v][m, unmapped]][v0][m0] ≠ unmapped → (avols[v, avols[v][m, unmapped]][v0][m0] = erased → avols0[v0][m0] = erased) ∧ (avols[v, avols[v][m, unmapped]][v0][m0].mapped? → avols0[v0][m0] = avols[v, avols[v][m, unmapped]][v0][m0])))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
# avols[v0] = # avols0[v0], m0 < # avols0[v0], m < # avols[v], ebm-cons(avols0), ebm-cons(avols), v0 ∈ avols0, v0 ∈ avols, v ∈ avols, ∀ m. m < # avols0[v0] ∧ avols[v0][m] ≠ unmapped → (avols[v0][m] = erased → avols0[v0][m] = erased) ∧ (avols[v0][m].mapped? → avols0[v0][m] = avols[v0][m]) ⊦ avols[v0][m0] = unmapped, v0 = v, (avols[v0][m0] = erased → avols0[v0][m0] = erased) ∧ (avols[v0][m0].mapped? → avols0[v0][m0] = avols[v0][m0])

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ v ≠ v0 → avols[v0, evol][v] = avols[v]; (s)% ⊦ v ≠ v0 → (v ∈ avols[v0, evol] ↔ v ∈ avols); (s)