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Proof step 13 from proof ebm-order-write-same (previous step)

v ∈ avols0, ∀ 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]))) ⊦ v0 = v, (v0 ∈ avols0 ↔ v0 ∈ avols1) ∧ ( v0 ∈ avols0 → # avols0[v0] = # avols1[v0] ∧ ( m0 < # avols0[v0] ∧ avols0[v0][m0] ≠ unmapped → (avols0[v0][m0] = erased → avols1[v0][m0] = erased) ∧ (avols0[v0][m0].mapped? → avols1[v0][m0] = avols0[v0][m0])))

User applied rule all left

And obtained the following new goals

Proof step 14:
v0 ∈ avols0 ↔ v0 ∈ avols1, v ∈ avols0, v0 ∈ avols0 → # avols0[v0] = # avols1[v0] ∧ (∀ m. m < # avols0[v0] ∧ avols0[v0][m] ≠ unmapped → (avols0[v0][m] = erased → avols1[v0][m] = erased) ∧ (avols0[v0][m].mapped? → avols1[v0][m] = avols0[v0][m])) ⊦ v0 = v, (v0 ∈ avols0 ↔ v0 ∈ avols1) ∧ ( v0 ∈ avols0 → # avols0[v0] = # avols1[v0] ∧ ( m0 < # avols0[v0] ∧ avols0[v0][m0] ≠ unmapped → (avols0[v0][m0] = erased → avols1[v0][m0] = erased) ∧ (avols0[v0][m0].mapped? → avols1[v0][m0] = avols0[v0][m0])))

Rule argument

pos: left 2 terms: v0 abort: F discard: T computed: F

Additional information

Used terms: v0