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Proof step 4 from proof ebm-order-write-same (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
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]))) ⊦ # avols0[v] = # avols1[v] ∧ ( m0 < # avols0[v] ∧ avols0[v][m, leb][m0] ≠ unmapped → (avols0[v][m, leb][m0] = erased → avols1[v][m, leb][m0] = erased) ∧ (avols0[v][m0].mapped? → avols1[v][m, leb][m0] = avols0[v][m, leb][m0]))

Rule argument

Additional information

Used simplifier rules: m ≠ n ⊦ evol[m, leb][n] = evol[n]; (s)% ⊦ 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% ⊦ m < # evol → evol[m, leb][m] = leb; (s)% ⊦ # evol[n, leb] = # evol; (s)% ⊦ avols[v, evol][v] = evol; (s)% ⊦ v ∈ avols[v, evol]; (s)