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Proof step 6 from proof ebm-order-trans (previous step)

v ∈ avols ↔ v ∈ avols0, v ∈ avols0 ↔ v ∈ avols1, v ∈ avols0 → # avols[v] = # avols0[v] ∧ (∀ m. m < # avols[v] ∧ avols[v][m] ≠ unmapped → (avols[v][m] = erased → avols0[v][m] = erased) ∧ (avols[v][m].mapped? → avols0[v][m] = avols[v][m])), v ∈ avols0 → # avols0[v] = # avols1[v] ∧ (∀ m. m < # avols0[v] ∧ avols0[v][m] ≠ unmapped → (avols0[v][m] = erased → avols1[v][m] = erased) ∧ (avols0[v][m].mapped? → avols1[v][m] = avols0[v][m])) ⊦ (v ∈ avols0 ↔ v ∈ avols1) ∧ ( v ∈ avols0 → # avols[v] = # avols1[v] ∧ ( m < # avols[v] ∧ avols[v][m] ≠ unmapped → (avols[v][m] = erased → avols1[v][m] = erased) ∧ (avols[v][m].mapped? → avols1[v][m] = avols[v][m])))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
# avols0[v] = # avols1[v], # avols[v] = # avols1[v], m < # avols1[v], v ∈ avols0, v ∈ avols1, v ∈ avols, ∀ m. m < # avols1[v] ∧ avols0[v][m] ≠ unmapped → (avols0[v][m] = erased → avols1[v][m] = erased) ∧ (avols0[v][m].mapped? → avols1[v][m] = avols0[v][m]), ∀ m. m < # avols1[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, (avols[v][m] = erased → avols1[v][m] = erased) ∧ (avols[v][m].mapped? → avols1[v][m] = avols[v][m])

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