[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 48 from proof swap-to-from-app (previous step)

⊦ #((σ to n0 + m) + σ0 from m) = #((σ to m + n0) from m) + # σ0, # σ < ⌜m⌝ + ⌜n0⌝ , # σ < ⌜n0⌝ + ⌜m⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ ⌜n⌝ < # σ ∧ finp(σ) → #(σ from n) = ⌜(# σ).n - n⌝
Proof step 50:
⊦ #((σ to n0 + m) + σ0 from m) = #((σ to m + n0) from m) + # σ0, # σ < ⌜n0⌝ + ⌜m⌝ , # σ < ⌜m⌝ + ⌜n0⌝ , ⌜m⌝ < #((σ to n0 + m) + σ0) ∧ finp((σ to n0 + m) + σ0)
Proof step 53:
⌜m⌝ < #((σ to n0 + m) + σ0), finp((σ to n0 + m) + σ0) ⊦ ⌜(#((σ to n0 + m) + σ0)).n - m⌝ = #((σ to m + n0) from m) + # σ0, # σ < ⌜n0⌝ + ⌜m⌝ , # σ < ⌜m⌝ + ⌜n0⌝

Rule argument

spec: <toplevel> name: fin-size-from seq: ⊦ ⌜n⌝ < # σ ∧ finp(σ) → #(σ from n) = ⌜(# σ).n - n⌝ subst: [n, σ] → [m, (σ to n0 + m) + σ0] flags: <all paths>

Additional information

Used terms: m, (σ to n0 + m) + σ0