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Proof step 64 from proof refine-remap (previous step)

m < # avols0[default-volid], ebm-cons(avols0), ebm-vol-inv(abs(avols0[default-volid])), default-volid ∈ avols0, ⌊err1⌋ ⊦ abs(avols0[default-volid])[m, unmapped] = abs(avols0[default-volid][m, unmapped]), abs(avols0[default-volid]) = abs(avols0[default-volid][m, unmapped])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 65:
⊦ avol = avol0 ↔ # avol = # avol0 ∧ (∀ n. n < # avol → avol[n] = avol0[n])
Proof step 66:
m < # avols0[default-volid], ebm-cons(avols0), ebm-vol-inv(abs(avols0[default-volid])), default-volid ∈ avols0, ⌊err1⌋ ⊦ abs(avols0[default-volid]) = abs(avols0[default-volid][m, unmapped]), # abs(avols0[default-volid])[m, unmapped] = # abs(avols0[default-volid][m, unmapped]) ∧ (∀ n. n < # abs(avols0[default-volid])[m, unmapped] → abs(avols0[default-volid])[m, unmapped][n] = abs(avols0[default-volid][m, unmapped])[n])

Rule argument

spec: array, inst: avolume name: Extension seq: ⊦ avol = avol0 ↔ # avol = # avol0 ∧ (∀ n. n < # avol → avol[n] = avol0[n]) subst: [avol0, avol] → [abs(avols0[default-volid][m, unmapped]), abs(avols0[default-volid])[m, unmapped]] flags: <all paths>

Additional information

Used terms: abs(avols0[default-volid][m, unmapped]), abs(avols0[default-volid])[m, unmapped]