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Proof step 12 from proof nodes-allocate (previous step)

gstore[m, groupblock([], [], m0)][m1] = groupblock(gndx, lax, m4) ⊦ m ∈ gstore, (m1 ∈ gstore[m, groupblock([], [], m0)] ∧ @(m2, m3) ∈ lax ∧ (m1 = m ∨ ¬ m1 ∈ ginval) → @(m1, m2, m3) ∈ gstore ∧ ¬ m1 ∈ ginval) ∧ ( m1 ∈ gstore[m, groupblock([], [], m0)] ∧ @(m2, m3) ∈ lax ∧ (m1 = m ∨ ¬ m1 ∈ ginval) → nodes(gstore[m, groupblock([], [], m0)], ginval -- m)[@(m1, m2, m3)] = nodes(gstore, ginval)[@(m1, m2, m3)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ n ∈ gstore[n0, gblock] ↔ n = n0 ∨ n ∈ gstore
Proof step 14:
gstore[m, groupblock([], [], m0)][m1] = groupblock(gndx, lax, m4) ⊦ m ∈ gstore, ((m1 = m ∨ m1 ∈ gstore) ∧ @(m2, m3) ∈ lax ∧ (m1 = m ∨ ¬ m1 ∈ ginval) → @(m1, m2, m3) ∈ gstore ∧ ¬ m1 ∈ ginval) ∧ ( (m1 = m ∨ m1 ∈ gstore) ∧ @(m2, m3) ∈ lax ∧ (m1 = m ∨ ¬ m1 ∈ ginval) → nodes(gstore[m, groupblock([], [], m0)], ginval -- m)[@(m1, m2, m3)] = nodes(gstore, ginval)[@(m1, m2, m3)])

Rule argument

spec: store, inst: group-store-ablock-store-nat-store name: In-insert seq: ⊦ n ∈ gstore[n0, gblock] ↔ n = n0 ∨ n ∈ gstore subst: [gblock, n0, gstore, n] → [groupblock([], [], m0), m, gstore, m1] flags: <all paths>

Additional information

Used terms: groupblock([], [], m0), m, gstore, m1