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Proof step 6 from proof abs-nodes-inv-flashsize-h (previous step)

# gndx0 + 1 = # lax, abs-nodes(buf, m, gnd ' + gndx0, lax, weak), ∀ buf0, m, gndx, lax, weak. # buf0 < # buf → abs-nodes(buf0, m, gndx, lax, weak) → inv-flashsize(gndx, lax) ⊦ inv-flashsize(gnd ' + gndx0, lax)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ abs-nodes(buf, m, gnd ' + gndx, lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, gnd ' + gndx, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, gnd) ∧ abs-nodes(buf1, m + # buf0, gndx, lax.tail, weak)))
Proof step 8:
# gndx0 + 1 = # lax, ∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, gnd ' + gndx0, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, gnd) ∧ abs-nodes(buf1, m + # buf0, gndx0, lax.tail, weak)), ∀ buf0, m, gndx, lax, weak. # buf0 < # buf → abs-nodes(buf0, m, gndx, lax, weak) → inv-flashsize(gndx, lax) ⊦ inv-flashsize(gnd ' + gndx0, lax)

Rule argument

spec: abs-list, inst: encoding-group-node name: abs-nodes-rec seq: ⊦ abs-nodes(buf, m, gnd ' + gndx, lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes (buf1, m + # buf0, gnd ' + gndx, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, gnd) ∧ abs-nodes (buf1, m + # buf0, gndx, lax.tail, weak))) subst: [weak, lax, gndx, gnd, m, buf] → [weak, lax, gndx0, gnd, m, buf] flags: <all paths>

Additional information

Used terms: weak, lax, gndx0, gnd, m, buf