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Proof step 32 from proof inv-gc (previous step)

# kx = # ax, replay(log0, fs0, fi, fo) = ri0 ⊖ ro, as ∩ ax.toSet = ∅, as ∩ log0.toSet = ∅, ax.toSet ∩ log0.toSet = ∅, as ∩ range ri0[kx, ax] = ∅, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0[ax, fs0[ri0[kx]]] \ as), log-cons(ax, fs0[ax, fs0[ri0[kx]]] \ as), log-cons(log0, fs0), new(ax, fs0), orphans-cons(fs0, ri0, ro), replay-safe(log0, fs0, fi ⊖ fo), ri-closed(ri0, fs0, ro), ri-cons(ri0[kx, ax], fs0[ax, fs0[ri0[kx]]] \ as), ri-cons(ri0, fs0), ri-inj(ri0[kx, ax]), ri-inj(ri0), ri-inj(fi), kx.toSet ⊆ dom ri0, ro ⊆ dom ri0, fo ⊆ dom fi ⊦ dups(ax), dups(kx), dups(log0), inodekey(0) ∈ ri0, ri-closed(ri0[kx, ax], fs0[ax, fs0[ri0[kx]]] \ as, ro) ∧ replay-safe(ax, fs0[ax, fs0[ri0[kx]]], replay-log(log0, fs0, fi ⊖ fo)) ∧ replay-log(ax, fs0[ax, fs0[ri0[kx]]], replay-log(log0, fs0, fi ⊖ fo)) = ri0[kx, ax] ⊖ ro ∧ file-node-cons(fs0[ax, fs0[ri0[kx]]] \ as, ri0[kx, ax]) ∧ orphans-cons(fs0[ax, fs0[ri0[kx]]] \ as, ri0[kx, ax], ro)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
# kx = # ax, replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, as ∩ ax.toSet = ∅, as ∩ log0.toSet = ∅, ax.toSet ∩ log0.toSet = ∅, as ∩ range ri0[kx, ax] = ∅, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0[ax, fs0[ri0[kx]]] \ as), log-cons(ax, fs0[ax, fs0[ri0[kx]]] \ as), log-cons(log0, fs0), new(ax, fs0), orphans-cons(fs0, ri0, ro), replay-safe(log0, fs0, fi ⊖ fo), ri-closed(ri0, fs0, ro), ri-cons(ri0[kx, ax], fs0[ax, fs0[ri0[kx]]] \ as), ri-cons(ri0, fs0), ri-inj(ri0[kx, ax]), ri-inj(ri0), ri-inj(fi), kx.toSet ⊆ dom ri0, ro ⊆ dom ri0, fo ⊆ dom fi ⊦ dups(ax), dups(kx), dups(log0), inodekey(0) ∈ ri0, ri-closed(ri0[kx, ax], fs0[ax, fs0[ri0[kx]]] \ as, ro) ∧ file-node-cons(fs0[ax, fs0[ri0[kx]]] \ as, ri0[kx, ax]) ∧ orphans-cons(fs0[ax, fs0[ri0[kx]]] \ as, ri0[kx, ax], ro)

Rule argument

Additional information

Used simplifier rules: # ax = # kx ⊦ ri-cons(ri, fs) ∧ kx.toSet ⊆ dom ri ∧ new(ax, fs) ∧ ¬ dups(ax) ∧ ¬ dups(kx) ∧ orphans-cons(fs, ri, ro) ∧ ri-closed(ri, fs, ro) ∧ ro.inodes? → replay-log(ax, fs[ax, fs[ri[kx]]], ri ⊖ ro) = ri[kx, ax] ⊖ ro; (s)%# ax = # kx ⊦ ri-cons(ri, fs) ∧ kx.toSet ⊆ dom ri ∧ new(ax, fs) ∧ ¬ dups(ax) ∧ ¬ dups(kx) ∧ orphans-cons(fs, ri, ro) ∧ ri-closed(ri, fs, ro) ∧ ro.inodes? → replay-safe(ax, fs[ax, fs[ri[kx]]], ri ⊖ ro); (s)% ⊦ replay(log, fs, fi, fo) = replay-log(log, fs, fi ⊖ fo); (s)