Nuprl Lemma : pi-par-decompose
∀[P:pi_term()]. P = pipar(pipar-left(P);pipar-right(P)) ∈ pi_term() supposing ↑pipar?(P)
Proof
Definitions occuring in Statement :
pipar-right: pipar-right(v),
pipar-left: pipar-left(v),
pipar?: pipar?(v),
pipar: pipar(left;right),
pi_term: pi_term(),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
assert_wf,
pipar?_wf,
le_wf,
pi_term_size_wf,
pi_term_wf,
int_seg_wf,
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,
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,
assert_elim,
pizero_wf,
bfalse_wf,
btrue_neq_bfalse,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
decidable__lt,
not-le-2,
subtract-is-less,
lelt_wf,
picomm_wf,
nat_wf,
pioption_wf,
pipar_wf,
pirep_wf,
pinew_wf,
not-equal-2,
le-add-cancel-alt,
sq_stable__le,
add-mul-special,
zero-mul
Latex:
\mforall{}[P:pi\_term()]. P = pipar(pipar-left(P);pipar-right(P)) supposing \muparrow{}pipar?(P)
Date html generated:
2015_07_23-AM-11_32_56
Last ObjectModification:
2015_01_29-AM-00_55_57
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