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Proof step 20 from proof refine-get-gc-block (previous step)

syn ↔ syn0, fi = fi1, fi0 = fi2, ginval = ginval2, gstore = gstore2, maxino = maxino0, n0 = n1, nx = nx0, remove-refsize0(istore1) = istore1, remove-refsize0(gstore2) = gstore2, elems nx0 ∩ ginval0 = ∅, dom gstore2 ∪ elems nx0 = dom gstore0 ∪ ginval0, btree-inv(rp, adr, istore2, istore1, zh, fi2, fi1), inv(istore1), inv(istore2), inv(gstore2), inv(gstore0 \ ginval0), ri-inj(fi1), ri-inj(fi2), n2 ∈ gstore0, n2 ∈ gstore2, istore1 ⊑ istore2, pstate = unbuffered → syn0, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → nx0 ≠ [] ∧ pstate.lnum = nx0.last ∧ pstate.lnum ∈ gstore0 ⊦ (∀ n. ¬(n ∈ dom gstore0 ∧ ¬ n ∈ nx)) ∧ ⟨err := ENOSPC⟩ (n2 = n0 ∧ ESUCCESS = err), ∃ n. (n ∈ dom gstore0 ∧ ¬ n ∈ nx) ∧ ⟨n0 := n; err := ESUCCESS⟩ (n2 = n0 ∧ ESUCCESS = err), dups(nx0), n2 ∈ nx0, n2 = n0 ∧ ESUCCESS = ENOSPC

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
remove-refsize0(gstore2) = gstore2, remove-refsize0(istore1) = istore1, elems nx0 ∩ ginval0 = ∅, dom gstore2 ∪ elems nx0 = dom gstore0 ∪ ginval0, btree-inv(rp, adr, istore2, istore1, zh, fi2, fi1), inv(gstore0 \ ginval0), inv(gstore2), inv(istore2), inv(istore1), ri-inj(fi2), ri-inj(fi1), n2 ∈ gstore0, n2 ∈ gstore2, istore1 ⊑ istore2, ¬ dups(nx0), ¬ n2 ∈ nx0, pstate.journal? → nx0 ≠ [] ∧ pstate.lnum = nx0.last ∧ pstate.lnum ∈ gstore0, pstate.index? → pstate.lnum ∈ istore2, pstate = unbuffered → syn0 ⊦ (¬ n ∈ gstore0 ∨ n ∈ nx0) ∧ ⟨err := ENOSPC⟩ (n2 = n0 ∧ ESUCCESS = err), ∃ n1. n1 ∈ gstore0 ∧ ¬ n1 ∈ nx0 ∧ ⟨n0 := n1; err := ESUCCESS⟩ (n2 = n0 ∧ ESUCCESS = err)

Rule argument

Additional information

Used simplifier rules: fwd-in-gstore0: ⊦ n ∈ gstore ∧ ¬ n ∈ nx ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → n ∈ gstore0; (forward) from specification apersistence-base%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]% ⊦ n ∈ dom gstore ↔ n ∈ gstore; (s)% ⊦ ESUCCESS ≠ ENOSPC; (s)