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Proof step 4 from proof initialization (previous step)

LEB_SIZE = LEB_SIZE, maxino6 = LEB_SIZE, maxino7 = maxino3, maxino8 = maxino2, zh0 = zh ⊦ [btree_format#(maxino3, LEB_SIZE, maxino2; adr, adr0, istore, istore0, ginval1, gstore1, gstore2, nx0, maxino4, ginval2, pstate, syn0; rp, err)] ( ( err = ESUCCESS → syn0 ∧ (∃ ri, fi. btree-inv(rp, adr0, istore, istore0, zh0, ri, fi)) ∧ inv-journal(nx0, gstore1, gstore2, ginval1) ∧ inv-index(istore, istore0) ∧ inv-state(pstate, nx0, gstore1, istore, syn0)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → btree-inv(rp, adr0, istore, istore0, zh0, ∅, ∅) ∧ gstore1 = ∅ ∧ ginval1 = ∅ ∧ maxino4 = maxino8 ∧ nx0 = [] ∧ ginval2 = ∅) → ( err = ESUCCESS → ⟨index_format#(maxino3, LEB_SIZE, maxino2; ; fi1, fi2, ginval3, gstore3, gstore4, nx1, maxino5, ginval4, syn1, err0)⟩ ( ginval3 = ginval1 ∧ gstore3 = gstore1 ∧ gstore4 = gstore2 ∧ nx1 = nx0 ∧ maxino5 = maxino4 ∧ ginval4 = ginval2 ∧ btree-inv(rp, adr0, istore, istore0, zh, fi1, fi2) ∧ ri = fi1 ∧ fi3 = fi2 ∧ (syn1 ↔ syn0) ∧ ESUCCESS = err0)) ∧ ( err ≠ ESUCCESS → (∀ fi, fi0, ginval, gstore, gstore0, nx, maxino, ginval0, syn. ⟨index_format#(maxino3, LEB_SIZE, maxino2; ; fi1, fi2, ginval3, gstore3, gstore4, nx1, maxino5, ginval4, syn1, err0)⟩ ( fi = fi1 ∧ fi0 = fi2 ∧ ginval = ginval3 ∧ gstore = gstore3 ∧ gstore0 = gstore4 ∧ nx = nx1 ∧ maxino = maxino5 ∧ ginval0 = ginval4 ∧ (syn ↔ syn1) ∧ err = err0))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ [btree_format#(maxino3, LEB_SIZE, maxino2; adr, adr0, istore, istore0, ginval1, gstore1, gstore2, nx0, maxino4, ginval2, pstate, syn0; rp, err)] ( ( err = ESUCCESS → syn0 ∧ (∃ ri, fi. btree-inv(rp, adr0, istore, istore0, zh, ri, fi)) ∧ inv(gstore1 \ ginval1) ∧ inv(gstore2) ∧ elems nx0 ∩ ginval1 = ∅ ∧ ¬ dups(nx0) ∧ dom gstore2 ∪ elems nx0 = dom gstore1 ∪ ginval1 ∧ remove-refsize0(gstore2) = gstore2 ∧ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0 ∧ (pstate.journal? → nx0 ≠ [] ∧ pstate.lnum = nx0.last ∧ pstate.lnum ∈ gstore1) ∧ (pstate.index? → pstate.lnum ∈ istore)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → btree-inv(rp, adr0, istore, istore0, zh, ∅, ∅) ∧ gstore1 = ∅ ∧ ginval1 = ∅ ∧ maxino4 = maxino2 ∧ nx0 = [] ∧ ginval2 = ∅) → ( err = ESUCCESS → ⟨index_format#(maxino3, LEB_SIZE, maxino2; ; fi1, fi2, ginval3, gstore3, gstore4, nx1, maxino5, ginval4, syn1, err0)⟩ ( ginval3 = ginval1 ∧ gstore3 = gstore1 ∧ gstore4 = gstore2 ∧ nx1 = nx0 ∧ maxino5 = maxino4 ∧ ginval4 = ginval2 ∧ btree-inv(rp, adr0, istore, istore0, zh, fi1, fi2) ∧ ri = fi1 ∧ fi3 = fi2 ∧ (syn1 ↔ syn0) ∧ ESUCCESS = err0)) ∧ ( err ≠ ESUCCESS → (∀ fi, fi0, ginval, gstore, gstore0, nx, maxino, ginval0, syn. ⟨index_format#(maxino3, LEB_SIZE, maxino2; ; fi1, fi2, ginval3, gstore3, gstore4, nx1, maxino5, ginval4, syn1, err0)⟩ ( fi = fi1 ∧ fi0 = fi2 ∧ ginval = ginval3 ∧ gstore = gstore3 ∧ gstore0 = gstore4 ∧ nx = nx1 ∧ maxino = maxino5 ∧ ginval0 = ginval4 ∧ (syn ↔ syn1) ∧ err = err0))))

Rule argument

Additional information

Used simplifier rules: ⊦ 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)%⊦ 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)