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Proof step 12 from proof nodes-ginval-rem (previous step)

gstore[m] = groupblock(gndx, lax, m2), dom gstore1 ⊆ dom gstore ⊦ (m ∈ gstore ∧ @(m0, m1) ∈ lax → (¬ m ∈ ginval \ dom gstore1 \ dom gstore ↔ ¬ m ∈ ginval)) ∧ ( m ∈ gstore ∧ @(m0, m1) ∈ lax ∧ ¬ m ∈ ginval \ 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 13:
⊦ n ∈ ns \ ns0 ↔ n ∈ ns ∧ ¬ n ∈ ns0
Proof step 14:
gstore[m] = groupblock(gndx, lax, m2), dom gstore1 ⊆ dom gstore ⊦ (m ∈ gstore ∧ @(m0, m1) ∈ lax → (¬(m ∈ ginval ∧ ¬ 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)])

Rule argument

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

Additional information

Used terms: dom gstore1 \ dom gstore, ginval, m