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Proof step 2 from proof inv-commit (previous step)

adr0 = adr, pstate = unbuffered, dom remove-refsize0(gstore) ∩ ginval = ∅, btree-inv(rp, adr, istore, istore0, zh, ri, fi), inv-index(istore, istore0), inv-journal(nx, gstore, gstore0, ginval), inv-state(pstate, nx, gstore, istore, syn) ⊦ ⟪btree_commit#(maxino, rp; ginval0, adr0, zh, adr, istore, istore0, ginval, gstore, gstore0, nx, maxino0, ginval1, pstate, syn; err)⟫ ( (∃ ri, fi. btree-inv(rp, adr, istore, istore0, zh, ri, fi)) ∧ inv-journal(nx, gstore, gstore0, ginval) ∧ inv-index(istore, istore0) ∧ inv-state(pstate, nx, gstore, istore, syn))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
adr0 = adr, pstate = unbuffered, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, syn, dom remove-refsize0(gstore) ∩ ginval = ∅, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, btree-inv(rp, adr, istore, istore0, zh, ri, fi), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), istore0 ⊑ istore, ¬ dups(nx) ⊦ ⟪btree_commit#(maxino, rp; ginval0, adr0, zh, adr, istore, istore0, ginval, gstore, gstore0, nx, maxino0, ginval1, pstate, syn; err)⟫ ( (∃ ri, fi. btree-inv(rp, adr, istore, istore0, zh, ri, fi)) ∧ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0 ∧ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn))

Rule argument

Additional information

Used simplifier rules: ⊦ inv-index(istore, istore0) ↔ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0; (s)%⊦ 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)% ⊦ ¬ unbuffered.index?; (s)% ⊦ ¬ unbuffered.journal?; (s)%⊦ 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)