[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 18 from proof inv-remove (previous step)

fi[key] = @(m, m0, m1), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, p_os < pmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, inv(gstore2 \ jro), inv(gstore1), refsize-cons(gstore2, range fi), refsize-cons(gstore1, range fi0), ri-inj(fi -- key), ri-inj(fi), ri-inj(fi0), key ∈ fi, pmaxino ≤ jmaxino, fi.lebs ⊆ dom gstore2, fi0.lebs ⊆ dom gstore1, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪index_get_gblock_refsize#(m, fi -- key, fi0, jro, gstore2, gstore1, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(m, n - m1, fi -- key, fi0, jro, gstore1, nx, pmaxino, p_os, jvalid0; gstore2)⟫ ( (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro)) ∧ (fi -- key).lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range(fi -- key)) ∧ inv(gstore2 \ jro) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro), pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
fi[key] = @(m, m0, m1), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, pmaxino ≠ 0, p_os < pmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, inv(gstore2 \ jro), inv(gstore1), refsize-cons(gstore2, range fi), refsize-cons(gstore1, range fi0), ri-inj(fi -- key), ri-inj(fi), ri-inj(fi0), key ∈ fi, m ∈ gstore2, pmaxino ≤ jmaxino, fi.lebs ⊆ dom gstore2, fi0.lebs ⊆ dom gstore1, ¬ dups(nx), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪index_get_gblock_refsize#(m, fi -- key, fi0, jro, gstore2, gstore1, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(m, n - m1, fi -- key, fi0, jro, gstore1, nx, pmaxino, p_os, jvalid0; gstore2)⟫ ( (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro)) ∧ (fi -- key).lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi -- @(m, m0, m1)) ∧ inv(gstore2 \ jro) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro)

Rule argument

Additional information

Used simplifier rules: ⊦ @(m, m0, m1).lnum = m; (s)%lebs-in-ri-in-gstore-explicit: ⊦ key ∈ ri ∧ ri[key] = adr ∧ ri.lebs ⊆ dom gstore → adr.lnum ∈ gstore; (forward) from specification gjournal-base%⊦ key ∈ ri ∧ ri[key] = adr ∧ ri-inj(ri) → range(ri -- key) = range ri -- adr; (s)