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Proof step 20 from proof range-rem-in (previous step)

ri[key0] = @(m, m0, m1), ri[key] = @(m, m0, m1), key-cons(key0, nodes(gstore, ginval)[@(m, m0, m1)]), key-cons(key, nodes(gstore, ginval)[@(m, m0, m1)]), @(m, m0, m1) ∈ gstore, key0 ∈ ri, key ∈ ri ⊦ key0 = key, m ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ key-cons(key, nd) ↔ nd.key = key ∧ (key.inode? → nd.inode? ∧ key.ino ≠ 0) ∧ (key.dentry? → nd.dentry?) ∧ (key.data? → nd.data?)
Proof step 22:
nodes(gstore, ginval)[@(m, m0, m1)].key = key, ri[key] = @(m, m0, m1), ri[key0] = @(m, m0, m1), key-cons(key0, nodes(gstore, ginval)[@(m, m0, m1)]), key ∈ ri, key0 ∈ ri, @(m, m0, m1) ∈ gstore, key.inode? → nodes(gstore, ginval)[@(m, m0, m1)].inode? ∧ key.ino ≠ 0, key.dentry? → nodes(gstore, ginval)[@(m, m0, m1)].dentry?, key.data? → nodes(gstore, ginval)[@(m, m0, m1)].data? ⊦ key0 = key, m ∈ ginval

Rule argument

spec: aubifs-inv name: key-cons seq: ⊦ key-cons(key, nd) ↔ nd.key = key ∧ (key.inode? → nd.inode? ∧ key.ino ≠ 0) ∧ (key.dentry? → nd.dentry?) ∧ (key.data? → nd.data?) subst: [nd, key] → [nodes(gstore, ginval)[@(m, m0, m1)], key] flags: <all paths>

Additional information

Used terms: nodes(gstore, ginval)[@(m, m0, m1)], key