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Proof step 3 from proof ebm-order-trans (previous step)

∀ 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]))), ∀ v. (v ∈ avols ↔ v ∈ avols0) ∧ ( v ∈ avols → # 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 ∈ avols ↔ v ∈ avols1) ∧ ( v ∈ avols → # 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])))

User applied rule all left

And obtained the following new goals

Proof step 4:
v ∈ avols ↔ v ∈ avols0, v ∈ avols → # 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. (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]))) ⊦ (v ∈ avols ↔ v ∈ avols1) ∧ ( v ∈ avols → # 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])))

Rule argument

pos: left 2 terms: v abort: F discard: T computed: F

Additional information

Used terms: v