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Proof step 17 from proof btree-inv-crash (previous step)

remove-refsize0(istore0) = istore0, ((btree(null, null, adr, height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh0), ((btree(null, rp, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh0), inv(istore), refsize-cons(istore, as), refsize-cons(istore0, as0), adr ∈ istore, nodes(istore0) ⊆ nodes(remove-refsize0(crash(istore, istore0))), as0 ⊆ alladrs0, as0 ⊆ dom nodes(istore0), as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), as0 ⊆ dom nodes(istore), istore0 ⊑ istore, ∃ r, zh, zbrar, dirty, nused. (null = null ⊃ ¬ dirty ∧ true(zh1);r = null ∧ zh = zh1) ∧ (dirty → false) ∧ (adr ∈ as0 ↔ ¬ dirty) ∧ adr ∈ alladrs0 ∧ nsize(nused, ok) ∧ unmodified(adr, mkznode(null, zbrar, height0 = 0, dirty, nused), nodes(istore0)) ∧ (( r => mkznode(null, zbrar, height0 = 0, dirty, nused) * bnode(r, zbrar, 0, nused, nused, height0, dirty, fi, nodes(istore0), as0 -- adr, alladrs0 -- adr) * true) )(zh) ⊦ adr ∈ remove-refsize0(crash(istore, istore0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
istore0[adr] = istore[adr], remove-refsize0(istore0) = istore0, ((btree(null, null, adr, height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh0), ((btree(null, rp, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh0), (( r => mkznode(null, zbrar, height0 = 0, false, nused) * bnode(r, zbrar, 0, nused, nused, height0, false, fi, nodes(istore0), as0 -- adr, alladrs0 -- adr) * true) )(zh), nused < BRANCH_SIZE, inv(istore), refsize-cons(istore, as), refsize-cons(istore0, as0), unmodified(adr, mkznode(null, zbrar, height0 = 0, false, nused), nodes(istore0)), adr ∈ as0, adr ∈ alladrs0, adr ∈ istore0, adr ∈ istore, nodes(istore0) ⊆ nodes(remove-refsize0(crash(istore, istore0))), as0 ⊆ alladrs0, as0 ⊆ dom nodes(istore0), as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), as0 ⊆ dom nodes(istore), istore0 ⊑ istore ⊦ # as0 = 0, # alladrs0 = 0, alladrs0 = ∅, as0 = ∅, adr ∈ remove-refsize0(crash(istore, istore0))

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ as ≠ ∅ → # as ≠ 0; (forward) from specification set-basic[node-store]%prefix-in: ⊦ adr ∈ istore ∧ istore ⊑ istore0 → adr ∈ istore0; (forward) from specification ablock-store-inv[index-store]%prefix-at: ⊦ adr ∈ istore ∧ istore ⊑ istore0 → istore[adr] = istore0[adr]; (forward) from specification ablock-store-inv[index-store]% ⊦ adr ∈ nodes(istore) ↔ adr ∈ istore; (s)%Dom: ⊦ adr ∈ dom iast ↔ adr ∈ iast; from specification store+set[index-store-address-store]% ⊦ BRANCH_SIZE ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%ne-01: ⊦ adr ∈ as → as ≠ ∅; (forward) from specification set-basic[node-store]%sub-in: ⊦ adr ∈ as ∧ as ⊆ as0 → adr ∈ as0; (forward) from specification set-basic[node-store]%trueH: ⊦ true(zh); from specification heap-sep[zheap]% ⊦ nsize(nused, ok) ↔ nused < BRANCH_SIZE; (s)