[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 4 from proof inv-remove-refsize0-diff (previous step)

st[n] = mkblock(x, lax, m), dom remove-refsize0(st) ∩ ns = ∅, n ∈ st, ∀ n. n ∈ st \ ns → # (st \ ns)[n].list = # (st \ ns)[n].ladrlist ∧ inv-flashsize((st \ ns)[n].list, (st \ ns)[n].ladrlist) ∧ ¬ dups((st \ ns)[n].ladrlist) ⊦ m = 0, inv-flashsize(x, lax) ∧ ¬ dups(lax)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 6:
st[n] = mkblock(x, lax, m), n ∈ st, ∀ n. n ∈ st \ ns → # (st \ ns)[n].list = # (st \ ns)[n].ladrlist ∧ inv-flashsize((st \ ns)[n].list, (st \ ns)[n].ladrlist) ∧ ¬ dups((st \ ns)[n].ladrlist), ∀ n. n ∈ dom remove-refsize0(st) ∩ ns ↔ n ∈ ∅ ⊦ m = 0, inv-flashsize(x, lax) ∧ ¬ dups(lax)

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [∅, dom remove-refsize0(st) ∩ ns] flags: <all paths>

Additional information

Used terms: ∅, dom remove-refsize0(st) ∩ ns