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Proof step 15 from proof nodes-ginval-rem-01 (previous step)

gstore[m] = groupblock(gndx, lax, m2), dom gstore1 ∪ ns = dom gstore ⊦ (m ∈ gstore ∧ @(m0, m1) ∈ lax → m ∈ dom gstore1 \ dom gstore → ¬ m ∈ ginval) ∧ ( m ∈ gstore ∧ @(m0, m1) ∈ lax ∧ (¬ m ∈ ginval ∨ m ∈ dom gstore1 \ dom gstore) → nodes(gstore, ginval \ dom gstore1 \ dom gstore)[@(m, m0, m1)] = nodes(gstore, ginval)[@(m, m0, m1)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ n ∈ ns \ ns0 ↔ n ∈ ns ∧ ¬ n ∈ ns0
Proof step 17:
gstore[m] = groupblock(gndx, lax, m2), dom gstore1 ∪ ns = dom gstore ⊦ (m ∈ gstore ∧ @(m0, m1) ∈ lax → m ∈ dom gstore1 ∧ ¬ m ∈ dom gstore → ¬ m ∈ ginval) ∧ ( m ∈ gstore ∧ @(m0, m1) ∈ lax ∧ (¬ m ∈ ginval ∨ m ∈ dom gstore1 ∧ ¬ m ∈ dom gstore) → nodes(gstore, ginval \ dom gstore1 \ dom gstore)[@(m, m0, m1)] = nodes(gstore, ginval)[@(m, m0, m1)])

Rule argument

spec: set-union, inst: nat-set name: Difference seq: ⊦ n ∈ ns \ ns0 ↔ n ∈ ns ∧ ¬ n ∈ ns0 subst: [ns0, ns, n] → [dom gstore, dom gstore1, m] flags: <all paths>

Additional information

Used terms: dom gstore, dom gstore1, m