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Proof step 14 from proof inv-gc (previous step)

# kx = # ax, fs = fs0[ax, fs0[ri0[kx]]], log = log0 + ax, ri = ri0[kx, ax], as ∩ range ri = ∅, log.toSet ∩ as = ∅, ax.toSet ∩ log0.toSet = ∅, fo.inodes?, ro.inodes?, log-cons(log0, fs0), new(ax, fs0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), kx.toSet ⊆ dom ri0 ⊦ dups(ax), dups(kx), log-cons(log0, fs \ as) ∧ log-cons(ax, fs \ as) ∧ ri-cons(ri0[kx, ax], fs \ as)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
# kx = # ax, as ∩ range ri0[kx, ax] = ∅, ax.toSet ∩ log0.toSet = ∅, as ∩ log0.toSet = ∅, as ∩ ax.toSet = ∅, ro.inodes?, fo.inodes?, log-cons(log0, fs0), new(ax, fs0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), kx.toSet ⊆ dom ri0 ⊦ dups(kx), dups(ax), log-cons(log0, fs0[ax, fs0[ri0[kx]]] \ as) ∧ log-cons(ax, fs0[ax, fs0[ri0[kx]]] \ as) ∧ ri-cons(ri0[kx, ax], fs0[ax, fs0[ri0[kx]]] \ as)

Rule argument

Additional information

Used simplifier rules: int-c: ⊦ as ∩ as0 = as0 ∩ as; from specification set-union[node-store]%int-a: ⊦ (as ∩ as0) ∩ as1 = as ∩ as0 ∩ as1; from specification set-union[node-store]%unc: ⊦ as ∪ as0 = as0 ∪ as; from specification set-union[node-store]%una: ⊦ (as ∪ as0) ∪ as1 = as ∪ as0 ∪ as1; from specification set-union[node-store]% ⊦ as ∩ (as0 ∪ as1) = ∅ ↔ as ∩ as0 = ∅ ∧ as ∩ as1 = ∅; (ws)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ (ax + ax0).toSet = ax.toSet ∪ ax0.toSet; (s)