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Proof step 8 from proof ebm-order-antisym (previous step)

# avols1[v] = # avols0[v], v ∈ avols0, v ∈ avols1, ∀ v. (v ∈ avols0 ↔ v ∈ avols1) ∧ ( 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]))), ∀ 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]

User applied rule all left

And obtained the following new goals

Proof step 9:
# avols1[v] = # avols0[v], v ∈ avols0 ↔ v ∈ avols1, v ∈ avols1, v ∈ avols0, 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])), ∀ 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]

Rule argument

pos: left 4 terms: v abort: F discard: T computed: F

Additional information

Used terms: v