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Proof step 9 from proof absf-at (previous step)

m0 < # ebatbl, # absf(v, evol, apebs, ebatbl, q, m0) < # ebatbl, # absf(v, evol, apebs, ebatbl, q, m0) ≤ m0, ∀ n, ebatbl, v, evol, apebs, q. n < m0 ∧ n < # ebatbl ∧ m0 ≤ # ebatbl → absf(v, evol, apebs, ebatbl, q, m0)[n] = (ebatbl[n] = unmapped ⊃ (v × n ∈ q ⊃ unmapped;erased) ;mapped(apebs[ebatbl[n].pnum].data, (evol[n].mapped? ⊃ evol[n].fill;apebs[ebatbl[n].pnum].fill)) ) ⊦ absf(v, evol, apebs, ebatbl, q, m0) [m0, (ebatbl[m0] = unmapped ⊃ (v × m0 ∈ q ⊃ unmapped;erased) ;mapped(apebs[ebatbl[m0].pnum].data, (evol[m0].mapped? ⊃ evol[m0].fill;apebs[ebatbl[m0].pnum].fill)) ) ] [m0 ] = (ebatbl[m0] = unmapped ⊃ (v × m0 ∈ q ⊃ unmapped;erased) ;mapped(apebs[ebatbl[m0].pnum].data, (evol[m0].mapped? ⊃ evol[m0].fill;apebs[ebatbl[m0].pnum].fill)) )

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: absf-size seq: ⊦ m ≤ # ebatbl → # absf(v, evol, apebs, ebatbl, q, m) = # ebatbl subst: [m, q, ebatbl, apebs, evol, v] → [m0, q, ebatbl, apebs, evol, v] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: m0, q, ebatbl, apebs, evol, v