Nuprl Lemma : pi-rank-pi-simple-subst-aux
∀[P:pi_term()]. ∀[t,x:Name]. ∀[avoid:Name List]. (pi-rank(pi-simple-subst-aux(t;x;P;avoid)) = pi-rank(P) ∈ ℤ)
Proof
Definitions occuring in Statement :
pi-simple-subst-aux: pi-simple-subst-aux(t;x;P;avoid),
pi-rank: pi-rank(p),
pi_term: pi_term(),
name: Name,
list: T List,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
list_wf,
name_wf,
nat_wf,
pi-rank_wf,
pi_term_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
zero-le-nat,
lelt_wf,
iff_weakening_equal,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
pi_term-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
unit_wf2,
unit_subtype_base,
it_wf,
pizero_wf,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
add_functionality_wrt_eq,
pi-simple-subst-aux_wf,
pi_prefix-ext,
le_antisymmetry_iff,
pi-replace_wf,
maybe-new_wf,
not_wf,
l_member_wf,
cons_wf,
squash_wf,
true_wf,
pi-rank-pi-replace
Latex:
\mforall{}[P:pi\_term()]. \mforall{}[t,x:Name]. \mforall{}[avoid:Name List].
(pi-rank(pi-simple-subst-aux(t;x;P;avoid)) = pi-rank(P))
Date html generated:
2015_07_23-AM-11_33_43
Last ObjectModification:
2015_02_04-PM-03_42_13
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