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Proof step 8 from proof refine-read-gnd (previous step)

gnd = gnd0, remove-refsize0(istore1) = istore1, remove-refsize0(gstore2) = gstore2, elems nx0 ∩ ginval0 = ∅, dom gstore2 ∪ elems nx0 = dom gstore0 ∪ ginval0, btree-inv(rp, adr1, istore2, istore1, zh, fi, fi0), inv(istore1), inv(istore2), inv(gstore2), inv(gstore0 \ ginval0), ri-inj(fi0), ri-inj(fi), @(m, m0, m1) ∈ gstore0, istore1 ⊑ istore2, ¬ dups(nx0), ¬ m ∈ ginval0, pstate = unbuffered → syn0, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → nx0 ≠ [] ∧ pstate.lnum = nx0.last ∧ pstate.lnum ∈ gstore0 ⊦ ⟪apersistence_read_gnd#(@(m, m0, m1), adr1, istore2, istore1, ginval0, gstore0, gstore2, nx0, maxino0, ginval2, pstate, syn0; gnd; err)⟫ ⟨index_read_gnd#(@(m, m0, m1), fi, fi0, ginval0, gstore0, gstore2, nx0, maxino0, ginval2, syn0; gnd0; err0)⟩ (gnd = gnd0 ∧ err = err0)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 9:
syn ↔ syn0, adr = adr1, adr0 = @(m, m0, m1), ginval = ginval2, gnd = gnd0, gstore = gstore2, istore = istore1, istore0 = istore2, maxino = maxino0, nx = nx0, remove-refsize0(gstore2) = gstore2, remove-refsize0(istore1) = istore1, elems nx0 ∩ ginval0 = ∅, dom gstore2 ∪ elems nx0 = dom gstore0 ∪ ginval0, btree-inv(rp, adr1, istore2, istore1, zh, fi, fi0), inv(gstore0 \ ginval0), inv(gstore2), inv(istore2), inv(istore1), ri-inj(fi), ri-inj(fi0), @(m, m0, m1) ∈ gstore0, istore1 ⊑ istore2, pstate.journal? → nx0 ≠ [] ∧ pstate.lnum = nx0.last ∧ pstate.lnum ∈ gstore0, pstate.index? → pstate.lnum ∈ istore2, pstate = unbuffered → syn0 ⊦ ⟪if adr0 ∈ gstore0 ∧ ¬ adr0.lnum ∈ ginval0 then {fail_or_success#(; ; err); if err = ESUCCESS then gnd := gstore0[adr0] else gnd := ?} else abort⟫ ⟨index_read_gnd#(@(m, m0, m1), fi, fi0, ginval0, gstore0, gstore2, nx0, maxino0, ginval2, syn0; gnd0; err0)⟩ (gnd = gnd0 ∧ err = err0), dups(nx0), m ∈ ginval0

Rule argument

pos: right 1

Additional information

Used simplifier rules: apersistence_read_gnd# (ADR, ROOTADR, ISTORE, ISTORE0, GINVAL, GSTORE, GSTORE0, NL, MAXINO, OS, PSTATE, PSYNCED ; GND ; ERR ) {if ADR ∈ GSTORE ∧ ¬ ADR.lnum ∈ GINVAL then {fail_or_success#(; ; ERR); if ERR = ESUCCESS then GND := GSTORE[ADR] else GND := ?} else abort };