Step
*
1
1
of Lemma
qeq-wf
1. r : Base
2. r1 : Base
3. r = r1 ∈ pertype(λr,s. ((r ∈ ℤ ⋃ (ℤ × ℤ-o)) ∧ (s ∈ ℤ ⋃ (ℤ × ℤ-o)) ∧ qeq(r;s) = tt))
4. r ∈ ℤ ⋃ (ℤ × ℤ-o)
5. r1 ∈ ℤ ⋃ (ℤ × ℤ-o)
6. qeq(r;r1) = tt
7. s : Base
8. s1 : Base
9. s = s1 ∈ pertype(λr,s. ((r ∈ ℤ ⋃ (ℤ × ℤ-o)) ∧ (s ∈ ℤ ⋃ (ℤ × ℤ-o)) ∧ qeq(r;s) = tt))
10. s ∈ ℤ ⋃ (ℤ × ℤ-o)
11. s1 ∈ ℤ ⋃ (ℤ × ℤ-o)
12. qeq(s;s1) = tt
13. ↑qeq(r;s)@i
⊢ ↑qeq(r1;s1)
BY
{ ((All (RWO "eqtt_to_assert<"))
THEN Auto
THEN (InstLemma `qeq-equiv` [] THEN D -1 THEN ExRepD THEN UseTrans ⌜s⌝⋅ THEN UseTrans ⌜r⌝⋅)) }
Latex:
Latex:
1. r : Base
2. r1 : Base
3. r = r1
4. r \mmember{} \mBbbZ{} \mcup{} (\mBbbZ{} \mtimes{} \mBbbZ{}\msupminus{}\msupzero{})
5. r1 \mmember{} \mBbbZ{} \mcup{} (\mBbbZ{} \mtimes{} \mBbbZ{}\msupminus{}\msupzero{})
6. qeq(r;r1) = tt
7. s : Base
8. s1 : Base
9. s = s1
10. s \mmember{} \mBbbZ{} \mcup{} (\mBbbZ{} \mtimes{} \mBbbZ{}\msupminus{}\msupzero{})
11. s1 \mmember{} \mBbbZ{} \mcup{} (\mBbbZ{} \mtimes{} \mBbbZ{}\msupminus{}\msupzero{})
12. qeq(s;s1) = tt
13. \muparrow{}qeq(r;s)@i
\mvdash{} \muparrow{}qeq(r1;s1)
By
Latex:
((All (RWO "eqtt\_to\_assert<"))
THEN Auto
THEN (InstLemma `qeq-equiv` [] THEN D -1 THEN ExRepD THEN UseTrans \mkleeneopen{}s\mkleeneclose{}\mcdot{} THEN UseTrans \mkleeneopen{}r\mkleeneclose{}\mcdot{}))
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