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Proof step 30 from proof crash-neutral-add-gnds (previous step)

(elems nx0 ∪ dom gstore0) ++ n = dom gstore ∪ ginval1, gstore[n] = groupblock(gndx0, lax0, m), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, ginval1 ∩ elems nx0 = ∅, inv(groupblock(gndx0, lax0, m)), inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ ginval1), n ∈ gstore, istore1 ⊑ istore2 ⊦ (⌊EIO⌋ ∨ EIO = ESUCCESS) ∧ ¬ dups(lax0 + []) ∧ # [] ≤ # gndx ∧ inv-flashsize(prefixn(# [], gndx), []) ∧ (EIO = ESUCCESS ↔ # [] = # gndx) ∧ ⟨ax := ([]).to-adr(journal((nx0 + n ').last).lnum), err0 := EIO; gstore2 := gstore [journal((nx0 + n ').last).lnum, gstore[journal((nx0 + n ').last).lnum].gndlist:= (gstore[journal((nx0 + n ').last).lnum].gndlist + prefixn(# [], gndx)) ]; gstore2[journal((nx0 + n ').last).lnum].ladrlist := gstore2[journal((nx0 + n ').last).lnum].ladrlist + []; if err0 ≠ ESUCCESS then ax := ?, pstate := readonly; syn := ?⟩ (syn ∧ crash(gstore, gstore0, ginval1, nx0 + n ') = crash(gstore2, gstore0, ginval1, nx0 + n ')), gndx = [], dups(nx0), n ∈ nx0, n ∈ ginval1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
(elems nx0 ∪ dom gstore0) ++ n = dom gstore ∪ ginval1, gstore[n] = groupblock(gndx0, lax0, m), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, ginval1 ∩ elems nx0 = ∅, gndx ≠ [], inv(gstore \ ginval1), inv(gstore0), inv(istore2), inv(istore1), inv(groupblock(gndx0, lax0, m)), n ∈ gstore, istore1 ⊑ istore2, ¬ dups(nx0), ¬ n ∈ ginval1, ¬ n ∈ nx0 ⊦ ⟨ax := ([]).to-adr(journal((nx0 + n ').last).lnum), err0 := EIO; gstore2 := gstore[journal((nx0 + n ').last).lnum, gstore[journal((nx0 + n ').last).lnum].gndlist:= gstore[journal((nx0 + n ').last).lnum].gndlist]; gstore2[journal((nx0 + n ').last).lnum].ladrlist := gstore2[journal((nx0 + n ').last).lnum].ladrlist; if err0 ≠ ESUCCESS then ax := ?, pstate := readonly; syn := ?⟩ (syn ∧ crash(gstore, gstore0, ginval1, nx0 + n ') = crash(gstore2, gstore0, ginval1, nx0 + n '))

Rule argument

Additional information

Used simplifier rules: a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gndx + [] = gndx; (s)% ⊦ # gndx = 0 ↔ gndx = []; (s)% ⊦ ESUCCESS ≠ EIO; (s)% ⊦ inv-flashsize([], lax) ↔ lax = []; (s)% ⊦ prefixn(0, gndx) = []; (s)% ⊦ 0 ≤ m; (s)% ⊦ # [] = 0; (s)% ⊦ inv(groupblock(gndx, lax, m0)) → ¬ dups(lax); (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ lax + [] = lax; (s)% ⊦ ⌊EIO⌋ ; (s)