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Proof step 7 from proof valid-group-nodes-shorter-prefix (previous step)

valid-group-nodes(prefixn(n0, gndx + gnd ')) < # prefixn(n, gndx + gnd '), valid-group-nodes(prefixn(n0, gndx + gnd ')) < valid-group-nodes(prefixn(n, gndx + gnd ')), n ≤ n0, ∀ n0, n1. valid-group-nodes(prefixn(n0, gndx)) < valid-group-nodes(prefixn(n1, gndx)) ∧ valid-group-nodes(prefixn(n0, gndx)) < # prefixn(n1, gndx) ∧ n1 ≤ n0 → gndx = [] ∨ n1 = 0 ⊦ n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
n ≤ # gndx ⊦ prefixn(n, gndx + gndx0) = prefixn(n, gndx)
Proof step 9:
valid-group-nodes(prefixn(n0, gndx + gnd ')) < valid-group-nodes(prefixn(n, gndx + gnd ')), valid-group-nodes(prefixn(n0, gndx + gnd ')) < # prefixn(n, gndx + gnd '), n ≤ n0, ∀ n0, n1. valid-group-nodes(prefixn(n0, gndx)) < valid-group-nodes(prefixn(n1, gndx)) ∧ valid-group-nodes(prefixn(n0, gndx)) < # prefixn(n1, gndx) ∧ n1 ≤ n0 → gndx = [] ∨ n1 = 0 ⊦ n = 0, n0 ≤ # gndx
Proof step 13:
valid-group-nodes(prefixn(n0, gndx)) < valid-group-nodes(prefixn(n, gndx + gnd ')), valid-group-nodes(prefixn(n0, gndx)) < # prefixn(n, gndx + gnd '), n ≤ n0, n0 ≤ # gndx, ∀ n0, n1. valid-group-nodes(prefixn(n0, gndx)) < valid-group-nodes(prefixn(n1, gndx)) ∧ valid-group-nodes(prefixn(n0, gndx)) < # prefixn(n1, gndx) ∧ n1 ≤ n0 → gndx = [] ∨ n1 = 0 ⊦ n = 0

Rule argument

spec: list-prefixn, inst: group-store name: prefixn-append-left seq: n ≤ # gndx ⊦ prefixn(n, gndx + gndx0) = prefixn(n, gndx) subst: [gndx0, gndx, n] → [gnd ', gndx, n0] flags: <all paths>

Additional information

Used terms: gnd ', gndx, n0