[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 6 from proof upto-less (previous step)

n ≤ m ⊦ (n0 * VFS_PAGE_SIZE < n ∧ n0 ∈ content → n0 * VFS_PAGE_SIZE < m) ∧ (n0 * VFS_PAGE_SIZE < n ∧ n0 * VFS_PAGE_SIZE < m ∧ n0 ∈ content → ((content upto m) upto n)[n0] = content[n0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ m * VFS_PAGE_SIZE < n ∧ m ∈ content → (content upto n)[m] = content[m]

Rule argument

spec: <toplevel> name: at-upto seq: ⊦ m * VFS_PAGE_SIZE < n ∧ m ∈ content → (content upto n)[m] = content[m] subst: [m, n, content] → [n0, n, content upto m] flags: <all paths>

Additional information

Used simplifier rules: in-upto: ⊦ m ∈ content upto n ↔ m * VFS_PAGE_SIZE < n ∧ m ∈ content;%in-upto: ⊦ m ∈ content upto n ↔ m * VFS_PAGE_SIZE < n ∧ m ∈ content;%at-upto: ⊦ m * VFS_PAGE_SIZE < n ∧ m ∈ content → (content upto n)[m] = content[m];%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s) Used terms: n0, n, content upto m