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Proof step 19 from proof btree-sub-clean-write-branches (previous step)

(r2 = r ⊃ mkznode(r0, zbrar[n, mkzbranch(key, adr, zbrar[n].child)], false, boolvar0, m);zh[r2]) = mkznode(r3, zbrar1, boolvar, true, m1), zh[r] = mkznode(r0, zbrar, false, boolvar0, m), zh[zbrar[n].child] = mkznode(r1, zbrar0, boolvar1, false, m0), zbrar[n, mkzbranch(key, adr, zbrar[n].child)][n0] = mkzbranch(key0, adr0, r2), n < # zbrar, n0 < m, n0 < # zbrar, r ∈ zh, r2 ∈ zh, n0 ≤ n, n0 < n ∧ zbrar[n0].branch? ∧ zbrar[n0].child ∈ zh → ¬ zh[zbrar[n0].child].dirty ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
(r2 = r ⊃ mkznode(r0, zbrar[n, mkzbranch(key, adr, zbrar[n].child)], false, boolvar0, m);zh[r2]) = mkznode(r3, zbrar1, boolvar, true, m1), zbrar[n, mkzbranch(key, adr, zbrar[n].child)][n0] = mkzbranch(key0, adr0, r2), zh[zbrar[n].child] = mkznode(r1, zbrar0, boolvar1, false, m0), zh[r] = mkznode(r0, zbrar, false, boolvar0, m), zh[zbrar[n0].child] = mkznode(r4, zbrar2, boolvar2, boolvar3, m2), n0 < # zbrar, n0 < m, n < # zbrar, r2 ∈ zh, r ∈ zh, n0 ≤ n, n0 < n ∧ zbrar[n0].branch? ∧ zbrar[n0].child ∈ zh → ¬ boolvar3 ⊦

Rule argument

spec: znode name: elim seq: ⊦ ( ( (r = znd.parent ∧ zbrar = znd.zbranches) ∧ (boolvar ↔ znd.leaf)) ∧ (boolvar0 ↔ znd.dirty)) ∧ m = znd.usedsize ↔ znd = mkznode(r, zbrar, boolvar, boolvar0, m) subst: [znd, r, zbrar, boolvar, boolvar0, m] → [zh[zbrar[n0].child], r4, zbrar2, boolvar2, boolvar3, m2]

Additional information

Used simplifier rules: ⊦ ( ( (r = znd.parent ∧ zbrar = znd.zbranches) ∧ (boolvar ↔ znd.leaf)) ∧ (boolvar0 ↔ znd.dirty)) ∧ m = znd.usedsize ↔ znd = mkznode(r, zbrar, boolvar, boolvar0, m); (elim) Used terms: zh[zbrar[n0].child], r4, zbrar2, boolvar2, boolvar3, m2