[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 2 from proof abs-istore-crash (previous step)

# lpt0 = # lpt, # avol0 = # lpt, n = # lpt0, dom istore ∩ elems nx = ∅, abs-istore(avol0, lpt, istore), flash-lpt-cons(lpt0, istore0, gstore0), synced(avol0), avol1 ↓ avol0, istore0 ⊑ istore ⊦ abs-istore(avol1, replay-lpt(replay-log(lpt0, nx), nx, n), remove-refsize0(crash(istore, istore0)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# avol0 = # lpt, # lpt0 = # lpt, dom istore ∩ elems nx = ∅, flash-lpt-cons(lpt0, istore0, gstore0), synced(avol0), avol1 ↓ avol0, istore0 ⊑ istore, ∀ n. (n < # lpt ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol0[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size) ⊦ ( n < # lpt ∧ replay-lpt(lpt0.mapIndices(elems nx, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx)), nx, # lpt)[n].flags = LP_INDEX_NODES ↔ n ∈ remove-refsize0(crash(istore, istore0))) ∧ ( n ∈ remove-refsize0(crash(istore, istore0)) → abs-leb (avol1[n], remove-refsize0(crash(istore, istore0))[n], replay-lpt(lpt0.mapIndices(elems nx, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx)), nx, # lpt)[n]) ∧ replay-lpt(lpt0.mapIndices(elems nx, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx)), nx, # lpt)[n].ref-size = remove-refsize0(crash(istore, istore0))[n].ref-size)

Rule argument

Additional information

Used simplifier rules: abs-istore-def: ⊦ abs-istore(avol, lpt, istore) ↔ (∀ n. (n < # lpt ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ ( n ∈ istore → abs-leb(avol[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size));%replay-log: ⊦ replay-log(lpt, nx) = lpt .mapIndices (elems nx, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx) );%replay-lpt-size: n ≤ # lpt ⊦ # replay-lpt(lpt, nx, n) = # lpt;% ⊦ ¬ n < n; (s)% ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ # lpt.mapIndices(ns, lptfun) = # lpt; (s)