Nuprl Lemma : permr_hd_cancel
∀T:Type. ∀a:T. ∀bs,bs':T List. (([a / bs] ≡(T) [a / bs']) ⇒ (bs ≡(T) bs'))
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
cons: [a / b],
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
permr: as ≡(T) bs,
cand: A c∧ B,
exists: ∃x:A. B[x],
top: Top,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
int_seg: {i..j-},
lelt: i ≤ j < k,
guard: {T},
uiff: uiff(P;Q),
subtract: n - m,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
sym_grp: Sym(n),
so_lambda: λ2x.t[x],
perm: Perm(T),
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
inv_funs: InvFuns(A;B;f;g),
tidentity: Id{T},
compose: f o g,
identity: Id,
perm_morph: perm_morph(S;T;s2t;t2s;p),
mk_perm: mk_perm(f;b),
perm_f: p.f,
pi1: fst(t),
tl_perm: tl_perm(p),
comp_perm: comp_perm,
txpose_perm: txpose_perm,
swap: swap(i;j),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
select: L[n],
cons: [a / b]
Lemmas referenced :
permr_wf,
cons_wf,
list_wf,
length_of_cons_lemma,
non_neg_length,
decidable__equal_int,
length_wf,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
perm_morph_wf,
int_seg_wf,
subtract_wf,
int_seg_properties,
decidable__le,
intformle_wf,
itermSubtract_wf,
int_formula_prop_le_lemma,
int_term_value_subtract_lemma,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
lelt_wf,
add-member-int_seg2,
tl_perm_wf,
add_nat_plus,
length_wf_nat,
less_than_wf,
nat_plus_wf,
nat_plus_properties,
equal_wf,
all_wf,
select_wf,
perm_f_wf,
nat_properties,
subtract-add-cancel,
add-subtract-cancel,
eq_int_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
perm_b_wf,
false_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
equal_symmetry,
perm_b_to_f,
perm_f_inj,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
squash_wf,
true_wf,
select-cons-tl,
add-is-int-iff,
equal-wf-base-T,
equal-wf-base,
select_cons_tl,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
cumulativity,
hypothesisEquality,
isectElimination,
hypothesis,
universeEquality,
productElimination,
independent_pairFormation,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
setElimination,
rename,
addEquality,
independent_functionElimination,
imageMemberEquality,
baseClosed,
applyLambdaEquality,
applyEquality,
equalityElimination,
impliesFunctionality,
instantiate,
hyp_replacement,
imageElimination,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion
Latex:
\mforall{}T:Type. \mforall{}a:T. \mforall{}bs,bs':T List. (([a / bs] \mequiv{}(T) [a / bs']) {}\mRightarrow{} (bs \mequiv{}(T) bs'))
Date html generated:
2017_10_01-AM-09_54_18
Last ObjectModification:
2017_03_03-PM-00_56_00
Theory : perms_2
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