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Proof step 3 from proof ubifs-cons-ri-inj (previous step)

ri[key] = ri[key0], ubifs-cons(fs, ri, ro, fi, fo, log), key ∈ ri, key0 ∈ ri ⊦ key = key0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ↔ ¬ inodekey(0) ∈ ri ∧ ri-cons(ri, fs) ∧ log-cons(log, fs) ∧ ¬ dups(log) ∧ ri-closed(ri, fs, ro) ∧ ro.inodes? ∧ fo.inodes? ∧ ro ⊆ dom ri ∧ fo ⊆ dom fi
Proof step 5:
ri[key] = ri[key0], ro.inodes?, fo.inodes?, log-cons(log, fs), ri-closed(ri, fs, ro), ri-cons(ri, fs), key0 ∈ ri, key ∈ ri, ro ⊆ dom ri, fo ⊆ dom fi ⊦ key = key0, dups(log), inodekey(0) ∈ ri

Rule argument

spec: <toplevel> name: ubifs-cons seq: ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ↔ ¬ inodekey(0) ∈ ri ∧ ri-cons(ri, fs) ∧ log-cons(log, fs) ∧ ¬ dups(log) ∧ ri-closed(ri, fs, ro) ∧ ro.inodes? ∧ fo.inodes? ∧ ro ⊆ dom ri ∧ fo ⊆ dom fi subst: [log, fo, fi, ro, ri, fs] → [log, fo, fi, ro, ri, fs] flags: <all paths>

Additional information

Used terms: log, fo, fi, ro, ri, fs