Nuprl Lemma : extend_perm_over_itcomp
∀n:ℕ. ∀ps:Sym(n) List. (↑{n}(Π ps) = (Π map(λp.↑{n}(p);ps)) ∈ Sym(n + 1))
Proof
Definitions occuring in Statement :
mon_reduce: mon_reduce,
extend_perm: ↑{n}(p),
sym_grp: Sym(n),
perm_igrp: perm_igrp(T),
map: map(f;as),
list: T List,
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
lambda: λx.A[x],
add: n + m,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
sym_grp: Sym(n),
or: P ∨ Q,
cons: [a / b],
le: A ≤ B,
less_than': less_than'(a;b),
colength: colength(L),
nil: [],
it: ⋅,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
subtype_rel: A ⊆r B,
mon_reduce: mon_reduce,
perm_igrp: perm_igrp(T),
mk_igrp: mk_igrp(T;op;id;inv),
grp_id: e,
pi2: snd(t),
pi1: fst(t),
infix_ap: x f y,
grp_op: *,
igrp: IGroup,
grp_car: |g|,
perm: Perm(T)
Lemmas referenced :
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
perm_wf,
int_seg_wf,
list-cases,
product_subtype_list,
colength-cons-not-zero,
colength_wf_list,
istype-false,
le_wf,
list_wf,
subtract-1-ge-0,
subtype_base_sq,
intformeq_wf,
int_formula_prop_eq_lemma,
set_subtype_base,
int_subtype_base,
spread_cons_lemma,
decidable__equal_int,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
itermAdd_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
int_term_value_add_lemma,
decidable__le,
nat_wf,
reduce_nil_lemma,
map_nil_lemma,
extend_perm_over_id,
reduce_cons_lemma,
map_cons_lemma,
equal_wf,
extend_perm_wf,
comp_perm_wf,
mon_reduce_wf,
perm_igrp_wf,
subtype_rel_self,
extend_perm_over_comp
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
universeIsType,
axiomEquality,
functionIsTypeImplies,
inhabitedIsType,
because_Cache,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
equalityIsType1,
dependent_set_memberEquality_alt,
instantiate,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
imageElimination,
equalityIsType4,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
intEquality,
hyp_replacement,
addEquality
Latex:
\mforall{}n:\mBbbN{}. \mforall{}ps:Sym(n) List. (\muparrow{}\{n\}(\mPi{} ps) = (\mPi{} map(\mlambda{}p.\muparrow{}\{n\}(p);ps)))
Date html generated:
2019_10_16-PM-01_01_51
Last ObjectModification:
2018_10_08-PM-00_44_44
Theory : list_2
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