Nuprl Lemma : hd_two_swap_permr
∀T:Type. ∀as:T List. ∀a,a':T. ([a; [a' / as]] ≡(T) [a'; [a / as]])
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
cons: [a / b],
list: T List,
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
permr: as ≡(T) bs,
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
int_seg: {i..j-},
lelt: i ≤ j < k,
txpose_perm: txpose_perm,
mk_perm: mk_perm(f;b),
perm_f: p.f,
pi1: fst(t),
sym_grp: Sym(n),
perm: Perm(T),
subtype_rel: A ⊆r B,
less_than: a < b,
squash: ↓T,
swap: swap(i;j),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
select: L[n],
cons: [a / b],
subtract: n - m,
bfalse: ff,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
length_of_cons_lemma,
istype-void,
length_wf,
istype-universe,
list_wf,
txpose_perm_wf,
add_nat_wf,
length_wf_nat,
istype-false,
le_wf,
nat_properties,
decidable__le,
add-is-int-iff,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
intformeq_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
false_wf,
non_neg_length,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
less_than_wf,
int_seg_wf,
select_wf,
cons_wf,
perm_f_wf,
int_seg_properties,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
select-cons-hd,
eqff_to_assert,
set_subtype_base,
lelt_wf,
int_subtype_base,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
equal_wf,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
select_cons_tl
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality_alt,
voidElimination,
hypothesis,
addEquality,
isectElimination,
hypothesisEquality,
natural_numberEquality,
independent_pairFormation,
inhabitedIsType,
universeIsType,
universeEquality,
dependent_pairFormation_alt,
dependent_set_memberEquality_alt,
equalityTransitivity,
equalitySymmetry,
because_Cache,
applyLambdaEquality,
setElimination,
rename,
unionElimination,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
baseClosed,
productElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
lambdaEquality_alt,
int_eqEquality,
equalityIsType1,
productIsType,
functionIsType,
applyEquality,
imageElimination,
equalityElimination,
equalityIsType2,
intEquality,
instantiate,
cumulativity,
productEquality,
imageMemberEquality
Latex:
\mforall{}T:Type. \mforall{}as:T List. \mforall{}a,a':T. ([a; [a' / as]] \mequiv{}(T) [a'; [a / as]])
Date html generated:
2019_10_16-PM-01_00_53
Last ObjectModification:
2018_10_08-AM-10_05_56
Theory : perms_2
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