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Proof step 4 from proof inv-commit-rec (previous step)

adr0 = adr1, istore1 = istore, pstate = index(m), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, zh[r0].dirty, pstate.index?, btree-inv(r0, adr1, istore, istore0, zh, ri, fi), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), r0 ∈ zh, m ∈ istore, istore0 ⊑ istore, pstate.journal? → nx ≠ [] ∧ m = nx.last ∧ m ∈ gstore ⊦ ⟪btree_commit_rec#(r0, adr1, istore0, ginval, gstore, gstore0, nx, ino, ns; adr1, err, zh, istore, pstate, bv)⟫ ( istore1 ⊑ istore ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → bv) ∧ inv(istore) ∧ istore0 ⊑ istore ∧ (err ≠ ESUCCESS → btree-inv(r0, adr0, istore, istore0, zh, ri, fi)) ∧ ( err = ESUCCESS → btree-inv(r0, adr1, istore, istore, zh, ri, ri) ∧ btree-inv (r0, adr0, istore[adr1.lnum, istore[adr1.lnum].ref-size:= (istore[adr1.lnum].ref-size - adr1.size)], istore0, zh[r0, zh[r0].dirty:= true], ri, fi) ∧ ¬ zh[r0].dirty)), pstate = unbuffered, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
adr0 = adr1, istore1 = istore, pstate = index(m), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, zh[r0].dirty, btree-inv(r0, adr1, istore, istore0, zh, ri, fi), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), m ∈ istore, r0 ∈ zh, istore0 ⊑ istore, ¬ dups(nx) ⊦ ⟪btree_commit_rec#(r0, adr1, istore0, ginval, gstore, gstore0, nx, ino, ns; adr1, err, zh, istore, pstate, bv)⟫ ( istore1 ⊑ istore ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → bv) ∧ inv(istore) ∧ istore0 ⊑ istore ∧ (err ≠ ESUCCESS → btree-inv(r0, adr0, istore, istore0, zh, ri, fi)) ∧ ( err = ESUCCESS → btree-inv(r0, adr1, istore, istore, zh, ri, ri) ∧ btree-inv (r0, adr0, istore[adr1.lnum, istore[adr1.lnum].ref-size:= (istore[adr1.lnum].ref-size - adr1.size)], istore0, zh[r0, zh[r0].dirty:= true], ri, fi) ∧ ¬ zh[r0].dirty))

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ index(m).journal?; (s)% ⊦ index(m).index?; (s)% ⊦ unbuffered ≠ index(m); (s)