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Proof step 6 from proof to-vtbl-update (previous step)

v ∈ vols ⊦ (v0 ∈ to-vtbl(vols -- v)[v, # vols[v]] ↔ v0 ∈ vols) ∧ to-vtbl(vols -- v)[v, # vols[v]][v0] = to-vtbl(vols)[v0]

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 7:
v ∈ vols ⊦ v0 = v, (v0 ∈ to-vtbl(vols -- v)[v, # vols[v]] ↔ v0 ∈ vols) ∧ to-vtbl(vols -- v)[v, # vols[v]][v0] = to-vtbl(vols)[v0]

Rule argument

fma: v0 = v

Additional information

Used simplifier rules: to-vtbl-at: ⊦ v ∈ vols → to-vtbl(vols)[v] = # vols[v];% ⊦ ¬ v ∈ vols → vols -- v = vols; (s)% ⊦ ¬ v ∈ vols → vols[v] = (∅)[v]; (s)% ⊦ v ∈ vtbl[v, n]; (s)% ⊦ vtbl[v, n][v] = n; (s) Used formulas: v0 = v