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Proof step 172 from proof inv-io-save (previous step)

zh[r] = mkznode(r0, zbrar, boolvar, true, m0), istore = istore3[m1, indexblock(save(mkznode(r0, zbrar, boolvar, true, m0)) ', @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', 0)], remove-refsize0(istore2) = istore2, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval2, ((btree(rp, r, adr1, height, dirty, ri, nodes(istore3), as, alladrs, ok) * P))(zh), n0 < save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize, btree-sub-clean(r, m0, zh), inv(istore3[m1, indexblock(save(mkznode(r0, zbrar, boolvar, true, m0)) ', @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', 0)]), inv(istore3[m1, indexblock([], [], 0)]), inv(istore2), inv(istore3), inv(gstore1), inv(gstore2 \ ginval2), refsize-cons(istore3, as0 ∪ as), m ∈ istore3, r ∈ zh, n0 ≤ LEB_SIZE, as ⊆ dom nodes(istore3), as ⊆ alladrs, alladrs ⊆ dom nodes(istore3), as0 ⊆ dom nodes(istore3), istore2 ⊑ istore3[m1, indexblock(save(mkznode(r0, zbrar, boolvar, true, m0)) ', @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', 0)], istore2 ⊑ istore3[m1, indexblock([], [], 0)], istore2 ⊑ istore3, ¬ dups(nx), ¬ adr1 ∈ as, ¬ m1 ∈ istore3, height = 0 → as = ∅ ⊦ ⟪apersistence_set_iblock_refsize# (index(m1).lnum, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize, adr0, istore2, ginval2, gstore2, gstore1, nx, maxino2, ginval, index(m1), syn ; istore); err0 := ESUCCESS; if err0 = ESUCCESS then zh[r].dirty := false⟫ ( refsize-cons(istore, as0 ∪ (err0 = ESUCCESS ⊃ as ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);as)) ∧ inv(istore) ∧ istore2 ⊑ istore ∧ m1 ∈ istore ∧ istore3 ⊑ istore ∧ r ∈ zh ∧ (err0 = ESUCCESS → ¬ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ∈ as) ∧ dom nodes(istore) = dom nodes(istore3) ∪ (err0 = ESUCCESS ⊃ ∅ ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);∅) ∧ (( btree (rp, r, (err0 = ESUCCESS ⊃ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);adr1), height, err0 ≠ ESUCCESS, ri, nodes(istore), (err0 = ESUCCESS ⊃ as ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);as), (err0 = ESUCCESS ⊃ (alladrs -- adr1) ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);alladrs), ok) * P) )(zh) ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ (err0 = ESUCCESS → ¬ zh[r].dirty))

User applied rule insert program lemma

And obtained the following new goals

Proof step 173:
inv-journal(nx, gstore, gstore0, ginval), inv-index(istore, istore0), inv-state(pstate, nx, gstore, istore, syn), maxino ∈ istore ⊦ ⟪apersistence_set_iblock_refsize#(maxino, n, adr, istore0, ginval, gstore, gstore0, nx, maxino0, ginval0, pstate, syn; istore)⟫ (inv-index(istore, istore0) ∧ inv-state(pstate, nx, gstore, istore, syn))
Proof step 174:
syn0 ↔ syn, zh[r] = mkznode(r0, zbrar, boolvar, true, m0), adr2 = adr0, ginval1 = ginval2, ginval3 = ginval, gstore3 = gstore2, gstore4 = gstore1, istore = istore3[m1, indexblock(save(mkznode(r0, zbrar, boolvar, true, m0)) ', @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', 0)], istore1 = istore2, maxino1 = index(m1).lnum, maxino3 = maxino2, n1 = save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize, nx0 = nx, pstate0 = index(m1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore2) = istore2, elems nx ∩ ginval2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval2, ((btree(rp, r, adr1, height, dirty, ri, nodes(istore3), as, alladrs, ok) * P))(zh), n0 < save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize, btree-sub-clean(r, m0, zh), inv(gstore2 \ ginval2), inv(gstore1), inv(istore3), inv(istore2), inv(istore3[m1, indexblock([], [], 0)]), inv(istore3[m1, indexblock(save(mkznode(r0, zbrar, boolvar, true, m0)) ', @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', 0)]), inv-index(istore, istore2), inv-journal(nx, gstore2, gstore1, ginval2), inv-state(index(m1), nx, gstore2, istore, syn), refsize-cons(istore3, as0 ∪ as), r ∈ zh, m ∈ istore3, index(m1).lnum ∈ istore, n0 ≤ LEB_SIZE, as0 ⊆ dom nodes(istore3), alladrs ⊆ dom nodes(istore3), as ⊆ alladrs, as ⊆ dom nodes(istore3), istore2 ⊑ istore3, istore2 ⊑ istore3[m1, indexblock([], [], 0)], istore2 ⊑ istore3[m1, indexblock(save(mkznode(r0, zbrar, boolvar, true, m0)) ', @(m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ', 0)], height = 0 → as = ∅ ⊦ [apersistence_set_iblock_refsize# (index(m1).lnum, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize, adr0, istore2, ginval2, gstore2, gstore1, nx, maxino2, ginval, index(m1), syn ; istore)] ( inv-index(istore, istore1) ∧ inv-state(pstate0, nx0, gstore3, istore, syn0) → ⟪err0 := ESUCCESS; if err0 = ESUCCESS then zh[r].dirty := false⟫ ( refsize-cons(istore, as0 ∪ (err0 = ESUCCESS ⊃ as ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);as)) ∧ inv(istore) ∧ istore2 ⊑ istore ∧ m1 ∈ istore ∧ istore3 ⊑ istore ∧ r ∈ zh ∧ (err0 = ESUCCESS → ¬ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize) ∈ as) ∧ dom nodes(istore) = dom nodes(istore3) ∪ (err0 = ESUCCESS ⊃ ∅ ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);∅) ∧ (( btree (rp, r, (err0 = ESUCCESS ⊃ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);adr1), height, err0 ≠ ESUCCESS, ri, nodes(istore), (err0 = ESUCCESS ⊃ as ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);as), (err0 = ESUCCESS ⊃ (alladrs -- adr1) ++ @(m1, m2, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize);alladrs), ok) * P) )(zh) ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ (err0 = ESUCCESS → ¬ zh[r].dirty))), dups(nx), adr1 ∈ as, m1 ∈ istore3

Rule argument

spec: apersistence-asm name: inv-set-iblock-refsize seq: inv-journal(nx, gstore, gstore0, ginval), inv-index(istore, istore0), inv-state(pstate, nx, gstore, istore, syn), maxino ∈ istore ⊦ ⟪apersistence_set_iblock_refsize# (maxino, n, adr, istore0, ginval, gstore, gstore0, nx, maxino0, ginval0, pstate, syn ; istore)⟫ ( inv-index(istore, istore0) ∧ inv-state(pstate, nx, gstore, istore, syn)) subst: [syn, pstate, ginval0, maxino0, nx, gstore0, gstore, ginval, istore0, adr, n, maxino, istore] → [syn, index(m1), ginval, maxino2, nx, gstore1, gstore2, ginval2, istore2, adr0, save(mkznode(r0, zbrar, boolvar, true, m0)).flashsize, index(m1).lnum, istore] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)%⊦ inv-index(istore, istore0) ↔ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0; (s)% ⊦ istore ⊑ istore0 ∧ ¬ n ∈ istore0 → istore ⊑ istore0[n, iblock]; (ss)%⊦ inv-state(pstate, nx, gstore, istore, syn) ↔ ( pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn); (s)% ⊦ ¬ index(m).journal?; (s)% ⊦ index(m).index?; (s)% ⊦ index(m).lnum = m; (s)% ⊦ n ∈ istore[n, iblock]; (s)% ⊦ unbuffered ≠ index(m); (s)