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Proof step 29 from proof crash-neutral-add-gnds (previous step)

(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 ∈ nx0, ¬ n ∈ ginval1 ⊦ ∃ lax, err. (⌊err⌋ ∨ err = ESUCCESS) ∧ ¬ dups(lax0 + lax) ∧ # lax ≤ # gndx ∧ inv-flashsize(prefixn(# lax, gndx), lax) ∧ (err = ESUCCESS ↔ # lax = # gndx) ∧ ⟨ax := lax.to-adr(journal((nx0 + n ').last).lnum), err0 := err; gstore2 := gstore [journal((nx0 + n ').last).lnum, gstore[journal((nx0 + n ').last).lnum].gndlist:= (gstore[journal((nx0 + n ').last).lnum].gndlist + prefixn(# lax, gndx)) ]; gstore2[journal((nx0 + n ').last).lnum].ladrlist := gstore2[journal((nx0 + n ').last).lnum].ladrlist + lax; if err0 ≠ ESUCCESS then ax := ?, pstate := readonly; syn := ?⟩ (syn ∧ crash(gstore, gstore0, ginval1, nx0 + n ') = crash(gstore2, gstore0, ginval1, nx0 + n '))

User applied rule exists right

And obtained the following new goals

Proof step 30:
(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

Rule argument

pos: right 1 terms: [], EIO abort: F discard: T computed: F

Additional information

Used terms: [], EIO