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Proof step 7 from proof ebm-order-trans (previous step)

# 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])

User applied rule all left

And obtained the following new goals

Proof step 8:
# avols[v] = # avols1[v], # avols0[v] = # avols1[v], m < # avols1[v], v ∈ avols, v ∈ avols1, v ∈ avols0, 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]), ∀ 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]) ⊦ 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 8 terms: m abort: F discard: T computed: F

Additional information

Used terms: m