[Imprint][Data Privacy Statement][E-Mail]

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Proof step 3 from proof id-idx-abs-gstore (previous step)

id-idx(lpt0, lpt1) ⊦ (∀ n. (n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt1[n])) ∧ (n ∈ gstore → lpt1[n].ref-size = gstore[n].ref-size)) ↔ (∀ n. (n < # lpt0 ∧ lpt0[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt0[n])) ∧ (n ∈ gstore → lpt0[n].ref-size = gstore[n].ref-size))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ id-idx(lpt1, lpt0) ↔ # lpt0 = # lpt1 ∧ (∀ n. n < # lpt0 → lpt1[n].ref-size = lpt0[n].ref-size ∧ lpt1[n].size = lpt0[n].size ∧ lpt1[n].flags = lpt0[n].flags)
Proof step 5:
# lpt1 = # lpt0, ∀ n. n < # lpt1 → lpt0[n].ref-size = lpt1[n].ref-size ∧ lpt0[n].size = lpt1[n].size ∧ lpt0[n].flags = lpt1[n].flags ⊦ (∀ n. (n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt1[n])) ∧ (n ∈ gstore → lpt1[n].ref-size = gstore[n].ref-size)) ↔ (∀ n. (n < # lpt0 ∧ lpt0[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt0[n])) ∧ (n ∈ gstore → lpt0[n].ref-size = gstore[n].ref-size))

Rule argument

spec: index-array, inst: gc-heap-base name: id-idx seq: ⊦ id-idx(lpt1, lpt0) ↔ # lpt0 = # lpt1 ∧ (∀ n. n < # lpt0 → lpt1[n].ref-size = lpt0[n].ref-size ∧ lpt1[n].size = lpt0[n].size ∧ lpt1[n].flags = lpt0[n].flags) subst: [lpt0, lpt1] → [lpt1, lpt0] flags: <all paths>

Additional information

Used terms: lpt1, lpt0