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Proof step 11 from proof to-vtbl-size (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ¬ v ∈ vtbl → # vtbl[v, n] = # vtbl + 1
Proof step 13:
∀ vols1. # vols1 < # vols0[v, ebatbl] → true → # to-vtbl(vols1) = # vols1 ⊦ # to-vtbl(vols0) + 1 = # vols0 + 1, v ∈ vols0, v ∈ to-vtbl(vols0)

Rule argument

spec: store, inst: vtbl name: Size-insert seq: ⊦ ¬ v ∈ vtbl → # vtbl[v, n] = # vtbl + 1 subst: [n, v, vtbl] → [# ebatbl, v, to-vtbl(vols0)] flags: <all paths>

Additional information

Used simplifier rules: to-vtbl-in: ⊦ v ∈ to-vtbl(vols) ↔ v ∈ vols;% ⊦ v ∈ vtbl → # vtbl[v, n] = # vtbl; (s) Used terms: # ebatbl, v, to-vtbl(vols0)