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Proof step 24 from proof btree-inv-crash (previous step)

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)), adr.lnum ∈ istore0 ∧ @(adr.pos, adr.size) ∈ crash(istore, istore0)[adr.lnum].ladrlist

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 25:
istore0[adr] = istore[adr], adr = @(m, m0, m1), remove-refsize0(istore0) = istore0, (( 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), ((btree(null, rp, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh0), ((btree(null, null, adr, height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh0), nused < BRANCH_SIZE, inv(istore), refsize-cons(istore0, as0), refsize-cons(istore, as), unmodified(adr, mkznode(null, zbrar, height0 = 0, false, nused), nodes(istore0)), adr ∈ istore, adr ∈ istore0, adr ∈ alladrs0, adr ∈ as0, as0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), as ⊆ dom nodes(istore), as ⊆ alladrs, as0 ⊆ dom nodes(istore0), as0 ⊆ alladrs0, nodes(istore0) ⊆ nodes(remove-refsize0(crash(istore, istore0))), istore0 ⊑ istore ⊦ # alladrs0 = 0, # as0 = 0, alladrs0 = ∅, as0 = ∅, adr ∈ remove-refsize0(crash(istore, istore0)), m ∈ istore0 ∧ @(m0, m1) ∈ crash(istore, istore0)[m].ladrlist

Rule argument

spec: address-data name: elim seq: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1) subst: [adr, m, m0, m1] → [adr, m, m0, m1]

Additional information

Used simplifier rules: ⊦ (m = adr.lnum ∧ m0 = adr.pos) ∧ m1 = adr.size ↔ adr = @(m, m0, m1); (elim) Used terms: adr, m, m0, m1