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Proof step 12 from proof ebm-order-antisym (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# avols1[v] = # avols0[v], n < # avols0[v], v ∈ avols1, v ∈ avols0, ∀ 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]), ∀ m. m < # avols0[v] ∧ avols1[v][m] ≠ unmapped → (avols1[v][m] = erased → avols0[v][m] = erased) ∧ (avols1[v][m].mapped? → avols0[v][m] = avols1[v][m]) ⊦ avols0[v][n] = avols1[v][n]

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