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Proof step 7 from proof absf-at (previous step)

m0 < # ebatbl, ∀ 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)) )

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 8:
m0 < # ebatbl, ∀ 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)) ), m0 < # absf(v, evol, apebs, ebatbl, q, m0)

Rule argument

fma: m0 < # absf(v, evol, apebs, ebatbl, q, m0)

Additional information

Used simplifier rules: ⊦ m < # evol → evol[m, leb][m] = leb; (s) Used formulas: m0 < # absf(v, evol, apebs, ebatbl, q, m0)