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Proof step 11 from proof nodes-allocate (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
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)])

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore[m, groupblock([], [], m0)][m1], gndx, lax, m4]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore[m, groupblock([], [], m0)][m1], gndx, lax, m4