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Proof step 8 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, 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 ⊦ ((btree(null, null, adr, height0, false, fi, nodes(remove-refsize0(crash(istore, istore0))), as0, alladrs0, ok) * true))(zh1) ∧ adr ∈ remove-refsize0(crash(istore, istore0)) ∧ alladrs0 ⊆ dom nodes(remove-refsize0(crash(istore, istore0)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ iast0 ⊆ iast1 ∧ ((btree(rp, r0, adr, height, dirty0, ri, iast0, as, alladrs, nstat) * P))(zh0) → ((btree(rp, r0, adr, height, dirty0, ri, iast1, as, alladrs, nstat) * P))(zh0)
Proof step 10:
remove-refsize0(istore0) = istore0, ((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), inv(istore), refsize-cons(istore0, as0), refsize-cons(istore, as), adr ∈ istore, as0 ⊆ dom nodes(istore), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), as ⊆ dom nodes(istore), as ⊆ alladrs, as0 ⊆ dom nodes(istore0), as0 ⊆ alladrs0, istore0 ⊑ istore ⊦ ((btree(null, null, adr, height0, false, fi, nodes(remove-refsize0(crash(istore, istore0))), as0, alladrs0, ok) * true))(zh1) ∧ adr ∈ remove-refsize0(crash(istore, istore0)) ∧ alladrs0 ⊆ dom nodes(remove-refsize0(crash(istore, istore0))), nodes(istore0) ⊆ nodes(remove-refsize0(crash(istore, istore0))) ∧ ((btree(null, null, adr, height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh1)
Proof step 13:
remove-refsize0(istore0) = istore0, ((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), ((btree(null, null, adr, height0, false, fi, nodes(istore0), as0, alladrs0, ok) * true))(zh1), inv(istore), refsize-cons(istore0, as0), refsize-cons(istore, as), adr ∈ istore, 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 ⊦ true ∧ adr ∈ remove-refsize0(crash(istore, istore0)) ∧ alladrs0 ⊆ dom nodes(remove-refsize0(crash(istore, istore0)))

Rule argument

spec: <toplevel> name: btree-istore-reduce seq: ⊦ iast0 ⊆ iast1 ∧ (( btree (rp, r0, adr, height, dirty0, ri, iast0, as, alladrs, nstat) * P) )(zh0) → (( btree (rp, r0, adr, height, dirty0, ri, iast1, as, alladrs, nstat) * P) )(zh0) subst: [iast0, zh0, P, nstat, alladrs, as, iast1, ri, dirty0, height, adr, r0, rp] → [nodes(istore0), zh1, true, ok, alladrs0, as0, nodes(remove-refsize0(crash(istore, istore0))), fi, false, height0, adr, null, null] flags: <all paths>

Additional information

Used terms: nodes(istore0), zh1, true, ok, alladrs0, as0, nodes(remove-refsize0(crash(istore, istore0))), fi, false, height0, adr, null, null