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Proof step 13 from proof to-vtbl-size (previous step)

∀ vols1. # vols1 < # vols0[v, ebatbl] → true → # to-vtbl(vols1) = # vols1 ⊦ # to-vtbl(vols0) + 1 = # vols0 + 1, v ∈ vols0, v ∈ to-vtbl(vols0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
∀ vols1. # vols1 < # vols0[v, ebatbl] → true → # to-vtbl(vols1) = # vols1 ⊦ # to-vtbl(vols0) = # vols0, v ∈ vols0

Rule argument

Additional information

Used simplifier rules: to-vtbl-in: ⊦ v ∈ to-vtbl(vols) ↔ v ∈ vols;%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)