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Proof step 47 from proof swap-to-from-app (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ ⌜n⌝ < # σ ∧ finp(σ) → #(σ from n) = ⌜(# σ).n - n⌝
Proof step 49:
¬(⌜m⌝ < #((σ to n0 + m) + σ0) ∧ finp((σ to n0 + m) + σ0)) ⊦ #((σ to n0 + m) + σ0 from m) = #((σ to m + n0) from m) + # σ0, # σ < ⌜n0⌝ + ⌜m⌝ , # σ < ⌜m⌝ + ⌜n0⌝
Proof step 52:
⌜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: inst: 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: rewrite, current

Additional information

Used terms: m, (σ to n0 + m) + σ0