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Proof step 23 from proof range-rem-in (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: nodes-gstore-at seq: ⊦ adr ∈ nodes(gstore, ginval) → nodes(gstore, ginval)[adr] = gstore[adr].nd subst: [adr, ginval, gstore] → [@(m, m0, m1), ginval, gstore] flags: <all paths>

Additional information

Used simplifier rules: nodes-gstore-in: ⊦ adr ∈ nodes(gstore, ginval) ↔ ¬ ¬(adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval);% ⊦ ¬ adr ∈ fs → fs[adr] = (∅)[adr]; (s)% ⊦ @(m, m0, m1).lnum = m; (s) Used terms: @(m, m0, m1), ginval, gstore