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Proof step 36 from proof abs-gstore-replay-lpt-unchanged (previous step)

# lpt = # avol1, # avol0 = # avol1, (n ∈ nx ∨ ¬ n ∈ ginval ⊃ groupblock(gstore[n].gndlist, gstore[n].ladrlist, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0));gstore0[n]) = groupblock(gndx, lax, m), n < # avol1 ∧ replay-lpt(lpt, nx, # avol1)[n].flags = LP_GROUP_NODES ↔ n ∈ crash(gstore, gstore0, ginval, nx), lpt[n] = mklp(m3, m4, lpf0, m5), replay-lpt(lpt, nx, # avol1)[n] = mklp(m0, m1, lpf, m2), n < # avol1 ∧ (n ∈ nx ∨ m3 ≠ 0 ∨ lpf0 = LP_FREE) → avol0[n] = avol1[n], n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], crash(gstore, gstore0, ginval, nx)[n], replay-lpt(lpt, nx, # avol1)[n]), n ∈ crash(gstore, gstore0, ginval, nx) → replay-lpt(lpt, nx, # avol1)[n].ref-size = (n ∈ nx ∨ ¬ n ∈ ginval ⊃ groupblock(gstore[n].gndlist, gstore[n].ladrlist, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0));gstore0[n]).ref-size ⊦ (n < # avol1 ∧ lpf = LP_GROUP_NODES ↔ n ∈ crash(gstore, gstore0, ginval, nx)) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol1[n], crash(gstore, gstore0, ginval, nx)[n], mklp(m0, m1, lpf, m2))) ∧ (n ∈ crash(gstore, gstore0, ginval, nx) → m0 = m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
# avol0 = # avol1, # lpt = # avol1, replay-lpt(lpt, nx, # avol1)[n] = mklp((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2), lpt[n] = mklp(m3, m4, lpf0, m5), n < # avol1, abs-leb (avol0[n], groupblock(gstore[n].gndlist, gstore[n].ladrlist, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0)), mklp((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2)), n ∈ gstore, n ∈ nx ∨ m3 ≠ 0 ∨ lpf0 = LP_FREE → avol0[n] = avol1[n] ⊦ abs-leb(avol1[n], crash(gstore, gstore0, ginval, nx)[n], mklp((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2)), n ∈ ginval

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%⊦ n ∈ crash(gstore, gstore0, ginval, nx) → crash(gstore, gstore0, ginval, nx)[n] = (n ∈ nx ∨ ¬ n ∈ ginval ⊃ groupblock (gstore[n].gndlist, gstore[n].ladrlist, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0)) ;gstore0[n] ); (s)% ⊦ ¬ n ∈ gstore → gstore[n] = (∅)[n]; (s)% ⊦ n ∈ crash(gstore, gstore0, ginval, nx) ↔ n ∈ gstore ∨ n ∈ ginval; (ws)%⊦ groupblock(gndx, lax, m) = groupblock(gndx0, lax0, m0) ↔ gndx = gndx0 ∧ lax = lax0 ∧ m = m0; (ws)% ⊦ groupblock(gndx, lax, m).ref-size = m; (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)